OPINION OF THE COURT
COWEN, Circuit Judge.
This appeal requires us to determine the standards for defining employment relationships under the Fair Labor Standards Act, “willful” violations of that statute, and the method for computing damages for such violations in the absence of employer records. The defendant in this case, a distributor of gasoline, oil, and related products, appeals the order of the United States District Court for the Western District of Pennsylvania determining that the operators of six gas stations were employees rather than independent contractors, and that defendant willfully violated the requirements of the Fair Labor Standards Act. Also before us is the award by the district court of liquidated damages to compensate the station operators for wages lost as a result of the statutory violations. Subject only to a minor mathematical adjustment, we will affirm the judgment of the district court.
I
The Secretary of Labor brought this action under the Fair Labor Standards Act, 29 U.S.C. §§ 201-219 (1988) (“FLSA” or “the Act”), to enjoin Selker Brothers, a distributor of gasoline, oil and other related products, from violating the Act’s minimum wage, overtime, recordkeeping and anti-retaliation provisions. The action also named Bernard Selker, the President of Selker Brothers, in his personal capacity. Following his death on April 15, 1991, his executrix, Helen Selker, was substituted as a party. We refer to the defendants collectively as “Selker.” The Secretary sought liquidated damages pursuant to section 216(c) of the Code, as well as back wages under the three-year statute of limitations set out in section 255(a), on the ground that Selker’s violations had been willfully committed.
Selker Brothers owned twenty gas stations, of which seven were directly operated by Bernard Selker and his family, five were leased, and eight were operated by commissioned operators. This appeal concerns six of the eight stations Selker classified as independent contractor stations. Two stations were in Franklin, Pennsylvania, one at Eighth and the other at Thirteenth Street. The remaining stations were located in Rimersburg, Seneca, Tionesta, and Snydersburg, Pennsylvania. It is stipulated that Selker owned the gas the stations sold, station operators had no investment in the gas, and Selker determined the price of gas at every station. The operators had keys to the pumps, but Selker did not give them the keys to the gasoline storage tanks. Nor did he allow the operators to paint cars or do body work at the stations.
The only compensation the station operators received from Selker was three cents commission on every gallon of gas sold and ten cents per gallon commission on sales of kerosene. This commission was not negotiable; it was set by Selker and could not be changed by the operators. For credit card sales of gasoline, operators were required by Selker to add a surcharge of three percent.
Each station had an island for pumping gas, a building for an office, as well as a sales area, storage area and garage. None of the station operators had written leases. The operators paid no rent, but did pay a portion of the stations’ monthly utilities, which Selker deducted from their commission checks along with other deductions for supplies, shortages and start up inventory. Selker controlled the hours of operation of each station and illumination of the stations at night. Selker maintained no records of the wages, hours, and other conditions of employment for the station operators or for other persons employed at the stations.
The Eighth Street Station in Franklin was run by Michael Cassano, who worked on average sixty hours per week, and employed workers to pump gas and do mechanical work. From July 20, 1986 through August 1988, Selker paid Cassano $19,826.01. Cassano supplemented these earnings by selling non-gasoline items including batteries, oil, candy and tobacco. His earnings from these sales averaged $400 per month. Bernard Selker fired Cas-sano and one of his assistants on August 31, 1988. Cassano testified that he complained to Bernard Selker that earnings based on commissions per gallon fell short of the minimum wage and Selker admitted the arrangement could be illegal. The district court found that Cassano and the assistant were fired because they complained to the Department of Labor about FLSA violations at the station.
The Thirteenth Street station was operated by William Koch from July 1986 through July 1989. Koch did not testify, but the district court found that he was paid a total of $21,520.37 in commissions during this three year period.
The Rimersburg station was an old-style station, a registered landmark with an old-fashioned pit but no lift. William McKinney operated this station from February 1986 through March 1988. From February 1986 to July 1987, he was paid on an hourly basis. In July 1987, Selker changed the method of payment to a commission basis. McKinney testified that the reason for the change, as explained to him by Bernard Selker, was that paying the hourly rate to the employees resulted in excessive overhead. From July 1987 to March 1988, McKinney was paid $7,202.21 in total commissions, and earned an average profit of $7.50 per month from the sale of non-gasoline items. McKinney testified that he used the pit as little as possible. He purchased the existing inventory of potato chips, soft drinks, candy, tobacco, motor oil and batteries from Selker at the time the station was converted to a commission basis. The district court found that Selker Brothers required McKinney to make this purchase. Upon terminating his tenure as station operator, McKinney sold the existing station inventory back to Selker Brothers.
Keith Zellefrow took over the operation of the Rimersburg station in April, 1988 and closed off the garage area to open a take-out restaurant. Zellefrow worked an average of 102 hours per week between April 1988 and January 1990, and was paid a total of $13,802.93 in commissions for gasoline sales.
The Tionesta station was run by six different operators between June 1986 and July 1988. Each received commissions from which station utility costs were deducted. Irvin Jenkins operated the station from June through August of 1986 but did not testify at trial. Keith Justice operated the Tionesta station from April 1987 through July 1987. He testified that he worked an average of 83 hours per week, and earned a total of approximately $270 per week from both gasoline and non-gasoline sales. The district court found that Justice worked an average of 98 hours per week for a total of 15 weeks and received commissions totalling $2,700.14. Based upon this estimate of hours worked, the district court awarded him $1,993.18 in back wages. Selker Brothers purchased the inventory when Justice quit.
The Snydersburg station was operated by Margaret and Roy Wolbert from May 1986 until December 18, 1987. The Wol-berts kept the station open from 7:00 a.m. to 9:00 p.m. Monday through Saturday, and from 9:00 a.m. to 9:00 p.m. on Sundays. They earned approximately $100 per month from mechanical work and approximately $10 per month from the sale, of non-gasoline items. Their son also worked at the station for a total of 37 weeks. The Wol-berts received commissions totalling $11,-608.29 between July 20, 1986 and December 1987. Raymond Hummell operated the Snydersburg station from April 1988 to June 1988. He made no profit from the sale of non-gasoline items, but earned a total of $480 by performing mechanical work. He worked 85 hours per week for total of eleven weeks and received commissions totalling $1,654.89.
The Seneca station was operated by Charles Kinear and his son Richard, from 1986 to March 1989. The station was open 94 hours per week. The Kinears rented the station garage to a mechanic, and received thirty percent of all labor performed, plus a mark-up on all parts used. In 1989, the Kinears sold their equipment to Al and Larry Stover, who performed their own mechanical work and hired others to pump gas. The district court found that the Department of Labor introduced insufficient evidence to substantiate the Ki-nears’ earnings and therefore assessed no damages. The Secretary has not appealed the district court’s findings with regard to this station.
The district court entered an order enjoining Selker from violating the minimum wage, overtime, retaliatory discharge and recordkeeping provisions of the FLSA. From the applicable findings of fact and conclusions of law, the sum of back wages due the aggrieved employees amounted to $142,220.91. The district court awarded liquidated damages in the amount of $140,-143.19. The court ordered Selker to pay the Secretary $280,286.38, an amount representing both the back wages and liquidated damages due.
II
The employment status of the station operators is a legal conclusion. Castillo v. Givens, 704 F.2d 181, 185-86 (5th Cir.), cert. denied, 464 U.S. 850, 104 S.Ct. 160, 78 L.Ed.2d 147 (1983). Thus our standard of review of the legal determination of employee status is plenary. United States v. Felton, 753 F.2d 276, 278 (3d Cir.1985). However, the district court’s findings of fact and the reasonable inferences in which it engaged are subject to the clearly erroneous standard. The factual findings underlying the district court’s computation and award of back wages are subject to the clearly erroneous standard. See United States v. Gambino, 864 F.2d 1064, 1071 n. 3 (3d Cir.), cert. denied, 492 U.S. 906, 109 S.Ct. 3215, 106 L.Ed.2d 566 (1989).
The statute of limitations to be applied in this case depends upon the court’s determination of whether Selker “willfully” violated the FLSA. The findings of fact underlying this determination are subject to the clearly erroneous standard of review. Whether Selker’s knowledge or intent amounted to willfulness under the statute is a question of law subject to plenary review.
The determination of good faith and reasonableness is a conclusion of law based upon findings of fact. Williams v. Tri County Growers, Inc., 747 F.2d 121, 129 n. 15 (3d Cir.1984); Smith v. Harris, 644 F.2d 985, 990 n. 1 (3d Cir.1981). The district court’s findings of fact and reasonable inferences therefrom are subject to the clearly erroneous standard, and its conclusions of law subject to plenary review. See Universal Minerals, Inc. v. C.A. Hughes & Co., 669 F.2d 98, 103 (3d Cir.1981); Schultz v. Wheaton Glass Co., 421 F.2d 259, 267 (3d Cir.), cert. denied, 398 U.S. 905, 90 S.Ct. 1696, 26 L.Ed.2d 64 (1970).
Ill
There is no single test to determine whether a person is an employee or an independent contractor for purposes of the FLSA. The statutory definitions regarding employment status are necessarily broad to effectuate the remedial purposes of the Act. See United States v. Rosenwasser, 323 U.S. 360, 363, 65 S.Ct. 295, 296-97, 89 L.Ed. 301 (1945); Donovan v. American Airlines, Inc., 686 F.2d 267, 271 (5th Cir.1982). The Act defines an employee as “any individual employed by an employer,” 29 U.S.C. § 203(e)(1) (1988), and an employer as “any person acting directly or indirectly in the interest of an employer in relation to an employee____” Id. § 203(d). In accordance with these expansive definitions, the Supreme Court has emphasized that the courts should look to the economic realities of the relationship in determining employee status under the FLSA. Rutherford Food Corp. v. McComb, 331 U.S. 722, 730, 67 S.Ct. 1473, 1477, 91 L.Ed. 1772 (1947).
It is a well-established principle that the determination of the employment relationship does not depend on isolated factors but rather upon the “circumstances of the whole activity.” Id. Courts have developed several criteria to assist them in determining the existence of an employment relationship under the Act. Although neither the presence nor the absence of any particular factor is dispositive, we have held that there are six factors to determine whether a worker is an “employee”:
1) the degree of the alleged employer’s right to control the manner in which the work is to be performed; 2) the alleged employee’s opportunity for profit or loss depending upon his managerial skill; 3) the alleged employee’s investment in equipment or materials required for his task, or his employment of helpers; 4) whether the service rendered requires a special skill; 5) the degree of permanence of the working relationship; 6) whether the service rendered is an integral part of the alleged employer’s business.
Donovan v. DialAmerica Marketing, Inc., 757 F.2d 1376, 1382 (3d Cir.), cert. denied, 474 U.S. 919, 106 S.Ct. 246, 88 L.Ed.2d 255 (1985). See also Donovan v. Sureway Cleaners, 656 F.2d 1368, 1370 (9th Cir.1981); Real v. Driscoll Strawberry Associates Inc., 603 F.2d 748, 754 (9th Cir.1979). Not only should courts examine the “circumstances of the whole activity,” they should “consider whether, as a matter of economic reality, the individuals ‘are dependent upon the business to which they render service.’ ” DialAmerica, 757 F.2d at 1382 (quoting Sureway Cleaners, 656 F.2d at 1370). See also Bartels v. Birmingham, 332 U.S. 126, 130, 67 S.Ct. 1547, 1550, 91 L.Ed. 1947 (1947); Usery v. Pilgrim Equipment Co., 527 F.2d 1308, 1311 (5th Cir.), cert. denied, 429 U.S. 826, 97 S.Ct. 82, 50 L.Ed.2d 89 (1976); Mednick v. Albert Enterprises, Inc., 508 F.2d 297, 299 (5th Cir.1975).
The district court applied the six-part multifactor “economic realities” test and concluded that an employment relationship between Selker and the station operators had been established. That conclusion was based upon the court’s analysis of the facts with respect to each of the established criteria for determining the existence of an FLSA employment relationship. Selker argues that these indicators support the contention that the station operators were independent contractors, not employees, and consequently, the district court’s findings should be set aside as clearly erroneous. We proceed to analyze the facts of this case as agreed to by the parties or found by the district court in light of the established criteria for determining employment vel non.
1. Control. The district court found that Selker had significant control over the manner in which the station operators performed their services. Because the sale of gas was not always the main profit center at each station, Selker contends that this finding was clearly erroneous. Selker argues that the operators were independent business people who had freedom to enter other activities such as the sale of convenience items and mechanical work, and who kept their own books and accounts with respect to their side businesses. Consequently, Selker argues, the stations were not really gas stations, but full service stations over which Bernard Selker exerted only limited control.
The record, in contrast, reflects Selker’s pervasive control over the stations in question. Selker set the price of cash sales of gasoline; station operators were required to make daily sales reports to Selker and to deposit the previous day’s receipts into a Selker Brothers bank account; station operators conducted their business operations without leases or written contracts; Bernard Selker visited each station regularly to oversee its operations; Selker controlled the hours of operation and the appearance of the stations; and he participated in decisions to hire and pay at least four mechanics. Collectively, the historic facts as agreed and those expressly found by the district court adequately support a finding of employer control over the day-to-day operations of the stations.
2. Opportunity for Profit or Loss. The district court concluded that the station operators had no meaningful opportunities for profit nor any significant risk of financial loss, because the volume of business depended upon the location of each station rather than upon the managerial skills of the operators. Selker points to three stations, Tionesta, Seneca and Rim-ersburg, where the relative success of each station changed, and argues that the professionalism of different operators increased the profit margin despite no change in location of the stations. Nonetheless, unlike truly independent station operators, who buy and resell gasoline for their own account, the earnings of these individuals were not tied to price levels and resale profit margins. On the contrary, the income of the various operators was derived primarily from their fixed commission from Selker. The evidence at trial showed that gasoline sales, non-gasoline sales, and mechanical work depended heavily upon the location of the station and the traffic volume flowing past the station. Since gasoline sales receipts were found to have been ten times the total receipts from the sale of non-gasoline items and mechanical work combined, the potential for profit from these side activities does not undermine the finding of the district court that the predominant money-making activity of the stations was the sale of gasoline.
3. Investment in Equipment and Employment of Workers. The district court found that the station operators had no significant investment in equipment and materials at their stations. Selker argues that it provided no inventory, tools or equipment, and therefore the investment of the operators was a function of their independent entrepreneurial incentive. The record, in contrast, shows that Selker Brothers required new station operators to obtain an inventory of supplies and equipment. Selker helped the operators fulfill this requirement by financing their inventory purchases and deducting from their semi-monthly commission checks pre-deter-mined amounts to be applied to those purchases. Selker reimbursed operators for all the gasoline and purchased inventory remaining at the termination of the operator’s service. The station operators had no capital investment in gasoline, which represented the single largest item in value carried by the stations. In view of these facts, the district court was justified in concluding that the operators’ side activities, which were merely incidental to the sale of gasoline, were irrelevant to the FLSA employment relationship arising from the predominant underlying business activity of selling gasoline. See Usery, 527 F.2d at 1313-14.
4. Special Skill. Though Selker concedes pumping gas requires no special skills, it maintains the stations were not just gas stations but rather all-around service stations, selling convenience items, auto supplies and mechanical services. Nevertheless, the predominant work performed was selling gas, and it was to that source that each operator looked for the mainstay of his or her income. “Routine work which requires industry and efficiency is not indicative of independence and nonemployee status.” Id. at 1314. Given the wide range of establishments selling gasoline on the highways, a distinction between service stations and gas stations may in some cases be valid, but the facts of this case adequately support the conclusion of the district court that the operators were employees. See Donovan v. Williams Oil Co., 717 F.2d 503 (10th Cir.1983); Marshall v. Truman Arnold, Distributing Co., Inc., 640 F.2d 906 (8th Cir.1981). In addition, the use of special skills is not itself indicative of independent contractor status, especially if the workers do not use those skills in any independent way. Brock v. Superior Care, Inc., 840 F.2d 1054, 1060 (2d Cir.1988). Given the degree of control exercised by Selker over the day-to-day operations of the stations, this criterion cannot be said to support a conclusion of independent contractor status.
5. Permanence of the Working Relationship. The district court found the station operators worked exclusively for Selker and their tenure appeared to have the length and continuity characteristic of employment. Selker asserts that the station operators were independent contractors because they built a client base for non-gasoline business they could take with them should their relationship with Selker terminate. It strains credulity to suggest that an operator’s “client base” for convenience items could be transferred to another station. Even if such a transfer could be made it would be irrelevant for the purpose of determining employment status in this case, given reliance of the operators on the sale of gas for the best part of their income. It cannot be said that the district court’s finding on this component of the multifactor test was clearly erroneous.
6. Integral Economic Relationship. The district court found that the sale of gasoline was an integral part of Selker’s business. Selker draws a distinction between the role of employees at the. seven stations operated directly by Bernard Selker and the six stations that are the subject of this case. At the seven stations operated directly by Selker, the employees pumped gas, made mechanical repairs, and sold convenience items, but did not make decisions regarding ongoing business operations. The operators of the six subject stations, Selker argues, were not an essential part of its operations, because when performing a tune-up or selling convenience items, they were not performing an activity that inured directly to Selker’s benefit. Selker characterizes non-gas sales as strictly personal to the station operator. Such a characterization disregards the purpose of offering convenience products and mechanical services, which was to attract gasoline customers to the stations. The primary business and economic purpose of the stations was to transact sales of gasoline.
In other service station cases where distributors have attempted to establish an independent contractor relationship in somewhat similar factual situations, courts have rejected such attempts, holding the workers to be employees of the distributors. See Williams Oil Co., 717 F.2d at 503; Marshall 640 F.2d at 906. The critical consideration in assessing the integral relationship factor is
the nature of the work performed by the workers: does that work constitute an “essential part” of the alleged employer’s business? In other words, regardless of the amount of work done, workers are more likely to be “employees” under the FLSA if they perform the primary work of the alleged employer.
DialAmerica, 757 F.2d at 1385 (citations omitted). Since Selker’s primary work was distributing and selling gasoline, and gasoline sales receipts constituted ninety percent of a station operator’s business, the integral economic relationship between Selker and the commissioned station operators was clearly one of employment. The district court correctly concluded that, as a matter of economic reality, the station operators were dependent upon Selker and, for purposes of the FLSA, were employees of Selker.
IV
The district court further concluded that Selker’s conduct was willful, and accordingly found that the applicable statute of limitations for enforcement of the FLSA was three years. Selker contends that the station operators were independent contractors, or, at the very least Bernard Selker reasonably believed the station operators to be independent contractors, and the applicable standard of limitations should be two years.
The controlling provision regarding the statute of limitations states in relevant part that
Any action ... to enforce any cause of action for unpaid minimum wages, unpaid overtime compensation, or liquidated damages, under the [FLSA] ... may be commenced within two years after the cause of action accrued, and every such action shall be forever barred unless commenced within two years after the cause of action accrued, except that a cause of action arising out of a willful violation may be commenced within three years after the cause of action accrued.
Portal-to-Portal Pay Act of 1947, 29 U.S.C. § 255(a). The Supreme Court set forth the standard which determines whether violations of the FLSA are willful in McLaughlin v. Richland Shoe Co., 486 U.S. 128, 108 S.Ct. 1677, 100 L.Ed.2d 115 (1988). There the Court held that an employer “willfully” violated the Act when it “knew or showed reckless disregard for the matter of whether its conduct was prohibited” by the Fair Labor Standards Act. Id. at 133, 108 S.Ct. at 1681. The Court adopted the same standard it had set in Trans World Airlines, Inc. v. Thurston, 469 U.S. 111, 105 S.Ct. 613, 83 L.Ed.2d 523 (1985), an Age Discrimination in Employment Act case, which defined a “willful” employer for liquidated damages purposes as one who shows a “disregard for the governing statute and an indifference to its requirements.” Id. at 127, 105 S.Ct. at 625.
Selker asserts that its conduct was reasonable, including its determination that the operators were independent contractors. The district court made a finding of fact that Bernard Selker knew paying employees on a commission basis could result in violations of the FLSA, and a conclusion of law that Selker displayed reckless disregard whether its conduct was prohibited by the FLSA. The court’s finding and conclusion are supported by the record. One operator testified that Bernard Selker told him there was a “fine line” regarding the legality of paying employees on a commission basis, and Selker instructed him to “hush it up.” App. at 253. Selker’s prior counsel testified that Bernard Selker expressed concern that “employees at the station [were] either not getting paid or [were] being paid in a way that he thought was inappropriate on a gallonage basis.” App. at 618. Selker adopted the commission system because “the overhead was too high on paying the hourly rate,” app. at 198, and then continued using it despite concerns and doubts as to its legality. Selker’s evident indifference toward the requirements imposed by the FLSA is fully consistent with the district court’s determination that Bernard Selker had willfully violated the Act.
V
A. Award of Back Wages In The Absence of Employer Records.
It is undisputed that Selker Brothers maintained no records of the wages, hours, and other conditions of employment for the station operators or their assistants. Because Selker failed to maintain adequate employer records as required by the FLSA, the district court permitted the Department of Labor to submit evidence from which violations of the Act and the amount of the award could reasonably be inferred. Selker contends that the district court’s calculation of damages was clearly erroneous.
The Supreme Court has instructed us how to calculate wages in the absence of employment records.
In such a situation [where the employer’s records are inadequate] we hold that an employee has carried out his burden if he proves that he has in fact performed work for which he was improperly compensated and if he produces sufficient evidence to show the amount and extent of that work as a matter of just and reasonable inference. The burden then shifts to the employer to come forward with evidence of the precise amount of work performed or with evidence to negative the reasonableness of the inference to be drawn from the employee’s evidence. If the employer fails to produce such evidence, the court may then award damages to the employee, even though the result may be only approximate.
Anderson v. Mt. Clemens Pottery, 328 U.S. 680, 687-88, 66 S.Ct. 1187, 1192-93, 90 L.Ed. 1515 (1946). The burden of any consequent imprecision from the absence of an employer’s records must be borne by that employer. “The employer cannot be heard to complain that the damages lack the exactness and precision of measurement that would be possible had he kept records in accordance with the requirements of § 11(c) of the Act.” Id. at 688, 66 S.Ct. at 1193. In such a situation, “the employer, having received the benefits of [the employees’] work, cannot object to the payment for the work on the most accurate basis possible under the circumstances.” Id. See also Williams, 747 F.2d at 128 (“[o]nce an employee establishes that the employer’s records are inadequate, the employee need only introduce enough evidence to support a reasonable inference of hours worked,” at which point the burden shifts to the employer to rebut that inference). In the absence of adequate employer records of employees’ wages and hours, as required by the FLSA, the solution is not to penalize the employees by denying recovery based on an inability to prove the extent of undercompensated work, but rather to allow the employee or the Secretary to submit sufficient evidence from which violations of the Act and the amount of an award may be reasonably inferred. See Mt. Clemens, 328 U.S. at 687, 66 S.Ct. at 1192.
The Department of Labor bore the burden of proving that the employees for whom relief was claimed were not properly compensated. It carried its burden by proving the operators in fact performed work for which they were not paid, and by producing sufficient evidence to show by reasonable inference the extent of that work and the amount of compensation the operators actually received. See id. at 688, 66 S.Ct. at 1193. Since Selker failed to keep adequate records of employment practices and conditions at the stations, the district court found that the commission earnings received by the station operators constituted sufficient evidence of their total earnings as a matter of just and reasonable inference. The burden accordingly shifted to Selker to come forward with evidence of the precise amount of earnings received and work performed by the operators or with evidence to negate the district court’s reasonable inferences based on the evidence. Id. at 687-88, 66 S.Ct. at 1192-93.
Selker Brothers failed to produce evidence at trial regarding the work performed and earnings received by the employees. The district court was well within its authority to award damages on behalf of the aggrieved employees, even though the result was approximate, because the uncertainty in awarding the damages was a result of Selker’s failure to keep records as required by the FLSA.
B. Award of Back Wages for Employees Who Did Not Testify.
The fact that William Koch and Irvin Jenkins did not testify does not render erroneous the district court’s findings of fact with regard to the Thirteenth Street or Tionesta stations. When an employer does not have accurate records, the employee need only show that he has in fact performed work for which he was not properly compensated, and produce sufficient evidence to show the amount and extent of that work as a matter of just and reasonable inference. See id.; Brock v. Norman’s Country Market, Inc., 835 F.2d 823, 828 (11th Cir.), cert. denied, 487 U.S. 1205, 108 S.Ct. 2845, 101 L.Ed.2d 883 (1988); Donovan v. Bel-Loc Diner, Inc., 780 F.2d 1113, 1116 (4th Cir.1985); Brennan v. General Motors Acceptance Corp. (“GMAC”), 482 F.2d 825, 829 (5th Cir.1973). It is not necessary for every single affected employee to testify in order to prove violations or to recoup back wages. The testimony and evidence of representative employees may establish prima facie proof of a pattern and practice of FLSA violations. See Donovan v. Simmons Petroleum Corp., 725 F.2d 83, 86 (10th Cir.1983) (testimony of twelve employees sufficient to support award for all former employees); Williams Oil Co., 717 F.2d at 504-05 (testimony of nineteen attendants sufficient to establish pattern of hours worked for thirty-four attendants at nine separate stations); GMAC, 482 F.2d at 829 (testimony of sixteen employees sufficient to support award for all thirty-seven employees); Marshall v. Brunner, 500 F.Supp. 116, 122 (W.D.Pa.1980) (testimony of forty-eight truck drivers working varying hours and receiving different amounts of pay sufficient to support award to ninety-three employees), aff'd, 668 F.2d 748 (3d Cir.1982).
Once the pattern or practice is established, the burden shifts to the employer to rebut the existence of the violations, Mt. Clemens, 328 U.S. at 687-688, 66 S.Ct. at 1192-93, or to prove that individual employees are excepted from the pattern or practice, GMAC, 482 F.2d at 829. Where employers have failed to comply with their statutory duty to keep adequate records, courts have resorted to documentary evidence as a basis for inferring hours worked. Williams Oil Co., 717 F.2d at 506 (back wage award partially based on gal-lonage records maintained by employer). In the absence of records and rebuttal evidence by Selker as to Koch’s average hourly work week, the district court had an adequate basis upon which to infer an average work week and sufficient documentary evidence as to gallonage with which to estimate damages. Documentary evidence exists as to the gallonage handled by William Koch at the Thirteenth Street station and at each of the other stations, from which an inference of hours worked can be made.
While it is true that neither William Koch nor any other employee testified as to operations at the Thirteenth Street station, the district court’s award of back wages to William Koch based upon the representative testimony of other Selker employees was not clearly erroneous.
Selker concedes that through the testimony of other representative operators, the court could reasonably infer that the Tionesta station was open ninety-five hours a week when Irvin Jenkins was the operator. Selker contends, however, that even though Jenkins’ station might have been open ninety-five hours a week, that does not mean he worked ninety-five hours. While this is perhaps true, it ignores the major principle of Mt. Clemens that, once the Secretary’s prima facie case is made, the burden shifts to the employer to dispute it with precise evidence of hours worked. This Selker has failed to do.
Selker disputes the ninety-eight hour average work week used by the district court in computing Keith Justice’s back wages. Indeed, Justice testified that he worked eighty-three hours per week. Since the record supports Selker’s contention as to Keith Justice, his back wage award must be reduced. Use of the eighty-three hour figure would reduce Selker’s back wage liability to this employee by $1,130.62, leaving a net liability of $862.56.
C. Full Liquidated Damages
The Secretary sought, and the district court awarded, liquidated damages equal to the back wages owed. Selker contends that only compensatory damages would be warranted since Bernard Selker believed his employees to be independent contractors. The district court found that Selker’s actions in establishing the operators as commission workers were not in good faith and he had no reasonable grounds for believing that such arrangements were valid under the FLSA. The evidence amply supports the factual findings of the district court that Bernard Selker knew he was violating the Act. Consequently, liquidated damages were mandatory.
The FLSA provides that “[a]n employer who violates the provisions of section 206 or section 207 ... shall be liable to the employees affected in the amount of their unpaid minimum wages, or their unpaid overtime compensation ... and in an additional amount as liquidated damages.” 29 U.S.C. § 216(b) (1988). These liquidated damages are compensatory rather than punitive in nature; they compensate employees for the losses they may have suffered by reason of not receiving their proper wages at the time they were due. See Overnight Motor Transp. Co. v. Missel, 316 U.S. 572, 583-84, 62 S.Ct. 1216, 1223, 86 L.Ed. 1682 (1942).
The governing rule for liquidated damages, 29 U.S.C. § 260 (1988), permits the district court “in its sound discretion” to award a lesser amount of liquidated damages, or none at all, “if the employer shows to the satisfaction of the court that the act or omission giving rise to the action was in good faith and that he had reasonable grounds for believing that his act or omission was not a violation of the Fair Labor Standards Act.” Id. To avoid liability for liquidated damages, the employer must make a showing of good faith and reasonable grounds for its conduct. If the employer fails to carry its burden of demonstrating good faith and reasonable grounds, the award of liquidated damages is mandatory. Dybach v. Florida Dep’t. of Corrections, 942 F.2d 1562, 1566-67 (11th Cir.1991); Brock v. Claridge Hotel and Casino, 846 F.2d 180, 187 (3d Cir.), cert. denied, 488 U.S. 925, 109 S.Ct. 307, 102 L.Ed.2d 326 (1988); Williams, 747 F.2d at 129; Marshall, 668 F.2d at 754; Barcelona v. Tiffany English Pub, 597 F.2d 464, 468 (5th Cir.1979).
The record is devoid of evidence showing good faith and reasonable grounds for Selker’s conduct. Despite Selker’s protestations to the contrary, the record supports the district court’s determination that the FLSA violations were willful. Selker has failed to carry its burden, and the district court’s award of liquidated damages will be affirmed subject only to a minor mathematical adjustment.
The district court awarded $140,143.19 in liquidated damages and doubled that amount to $280,286.38 for its total monetary award in the final judgment. When the specific back wage awards are totalled, however, they amount to $142,220.91. Instead of doubling the back wage total, the district court awarded some $2,077.72 less than that total as liquidated damages. To correct this minor discrepancy, and taking the reduction in Keith Justice’s back wages into consideration, the award for ■ back wages must be reduced by .99 percent. In all other respects, the judgment of the district court will be affirmed.
. The seven stations operated directly by Selker Brothers were full service stations, staffed with employees who were paid an hourly rate in excess of the minimum wage and time and a half for overtime.
. The Department of Labor originally brought suit on behalf of the employees of all eight stations classified by Selker as independent con-trador stations. At the outset of the trial, however, the Department of Labor dropped its claims on behalf of two of the eight stations.
.The employees at each station to whom the district court awarded back wages are listed infra note 9.
. Selker has not pressed on appeal the finding by the district court that Cassano and his assistant were wrongfully discharged. While the issue of retaliatory discharge has been abandoned, Selker does challenge on appeal the district court's specific back pay award to Michael Cassano in connection with his discharge. Since the district court denied back wages for his "wrongful termination,” and no appeal was taken by the Secretary as to this employee, neither the circumstances attending his discharge nor the loss of wages resulting therefrom is before this Court. Jackson v. University of Pittsburgh, 826 F.2d 230, 237 (3d Cir.1987), cert. denied, 484 U.S. 1020, 108 S.Ct. 732, 98 L.Ed.2d 680 (1988); Brown v. Sielaff, 474 F.2d 826, 828 (3d Cir.1973).
. The district court’s erroneously high estimate of the hours Keith Justice worked was the result of a discrepancy between the hours he reported and the estimate given by Department of Labor counsel. The discrepancy arose during the testimony as follows:
Q: [W]hat were your hours at the station being operated?
A: We were running during the week eight to eight. On the weekend, eight to nine. Oh— well, Friday night and Saturday it was eight to nine, and Sunday I didn't open 'til nine and we usually closed about six. Some days we were there a little longer. Some days, if it was really slow, like a Wednesday or Thursday afternoon was really slow, I went home.
Q: You were working approximately ninety-eight hours a week?
A: No, that’s — I'd say that’s quite a few hours.
Q: Well, that’s as many hours as you’ve just testified to. Were you there the whole time?
A: Yes.
App. at 517-18. The district court evidently used the 98 hour estimate of Department of Labor counsel in calculating damages of $6,381.75. The correct calculation of 83 hours per week for 15 weeks produces damages of $5,251.13, a difference of $1,130.62.
. The figure awarded by the court, $280,286.38, is exactly double the amount of liquidated damages ($140,143.19). The statute calls for liquidated damages equal to double the amount of back wages. 29 U.S.C. § 216(b). The district court presumably intended to double the total back wage award of $142,220.91 for liquidated damages purposes, but used the figure $140,-143.19 instead. Taking this minor discrepancy and the reduction in Keith Justice’s back wages into consideration, the back wage awards will be reduced by a mathematical factor (.99 percent) arrived at by dividing the liquidated damages total by the back wage total, so as to match the two totals. The total monetary award is set out infra note 9.
. Selker’s brief points to a major investment in wrecking equipment made at a Selker Brothers station in Marienville. Brief of Appellant at 20, 26. The Secretary dropped her claim regarding the Marienville station at the outset of the trial.
. The figure used for purposes of setting the total monetary award herein was set forth and argued by the Secretary to remedy the miscalculations of the district court. For explanation of the mathematical factor of .99 percent, see note 6 supra. The Secretary’s methodology for recomputing back wages was neither challenged by Selker in briefing nor at oral argument, hence for appellate purposes the mathematical process suggested by the Secretary is not disputed. See Jackson v. University of Pittsburgh, 826 F.2d 230, 237 (3d Cir.1987). The corrected back wage totals are given in note 9, infra, rendering unnecessary any remand.
. The eighteen specific back wage awards must be reduced by a mathematical figure of .99 percent, arrived at by dividing the liquidated damages total by the back wage total, so as to match the two totals, thus:
District Court Back Wage Back Wages Station Employee Award X .99
8th Street, M. Cassano $20,258.92 $20,122.93
Station Employee District Court Back Wage Award Back Wages X .99 V
Franklin C. Umstead 673.50 668.98
M. Monks 2,096.00 2,081.93
W. Hale 165.00 163.89
13th Street, Franklin W. Koch 46,071.68 45,762.42
Rimersburg W. McKinney 8,686.41 8,628.10
K. Zellefrow 32,921.74 32,700.75
Tionesta F. Harkless 7.191.18 7,142.91
I. Jenkins 583.14 579.23
J. Guthrie 1,447.87 1,438.15
J. Preisel 2.077.72 2.063.77
K. Preisel 2.077.72 2.063.77
K. Justice 862.56 856.77
Snydersburg M. Wolbert 4,502.40 4,472.18
R. Wolbert 5.468.18 5,431.47
T. Wolbert 3,470.60 3,447.30
R. Hummel 1,982.92 1,969.61
P. Hummel 552.75 549.04
$141,090.29 $140,143.20
No money damages were assessed against the Seneca station.
The mathematical factor .99 is arrived at by dividing the liquidated damages total by the back wage total, so as to match the two totals.
The district court awarded $1,993.18 in back wages to Keith Justice, based upon an erroneous overestimate of hours worked. The correct figure, listed above, is $862.56.