GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 21 Nov 2019, 22:49

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Three printing presses, R, S, and T, working together at the

Author Message
TAGS:

### Hide Tags

VP
Joined: 14 Dec 2004
Posts: 1190
Three printing presses, R, S, and T, working together at the  [#permalink]

### Show Tags

Updated on: 17 Sep 2013, 07:25
5
33
00:00

Difficulty:

5% (low)

Question Stats:

91% (01:21) correct 9% (02:14) wrong based on 1517 sessions

### HideShow timer Statistics

Three printing presses, R, S, and T, working together at their respective constant rates, can do a certain printing job in 4 hours. S and T, working together at their respective constant rates, can do the same job in 5 hours. How many hours would it take R, working alone at its constant rate, to do the same job?

A. 8
B. 10
C. 12
D. 15
E. 20

Originally posted by vivek123 on 04 Mar 2006, 12:41.
Last edited by Bunuel on 17 Sep 2013, 07:25, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8456
Location: United States (CA)
Re: Three printing presses, R, S, and T, working together at the  [#permalink]

### Show Tags

06 Dec 2016, 08:23
6
4
vivek123 wrote:
Three printing presses, R, S, and T, working together at their respective constant rates, can do a certain printing job in 4 hours. S and T, working together at their respective constant rates, can do the same job in 5 hours. How many hours would it take R, working alone at its constant rate, to do the same job?

A. 8
B. 10
C. 12
D. 15
E. 20

We are given that three printing presses, R, S, and T, working together at their respective constant rates, can do a certain printing job in 4 hours.

We can let r, s and t be the times, in hours, for printing presses R, S and T to complete the job alone at their respective constant rates. Thus, the rate of printing press R = 1/r, the rate of printing press S = 1/s, and the rate of printing press T = 1/t. Recall that rate = job/time and, since they are completing one printing job, the value for the job is 1. Since they complete the job together in 4 hours, the sum of their rates is 1/4, that is:

1/r + 1/s + 1/t = 1/4

We are also given that printing presses S and T, working together at their respective constant rates, can do the same job in 5 hours. Thus:

1/s + 1/t = 1/5

We can substitute 1/5 for 1/s + 1/t is the equation 1/r + 1/s + 1/t = 1/4 and we have:

1/r + 1/5 = 1/4

1/r = 1/4 - 1/5

1/r = 5/20 - 4/20

1/r = 1/20

r = 20

Thus, it takes printing press R 20 hours to complete the job alone.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

VP
Joined: 02 Jul 2012
Posts: 1099
Location: India
Concentration: Strategy
GMAT 1: 740 Q49 V42
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: RTD - Combined Worked Sum  [#permalink]

### Show Tags

01 Dec 2012, 05:43
17
4
SreeViji wrote:
Three printing presses, R, S, and T, working together at their respective constant rates, can do a certain printing job in 4 hours. S and T, working together at their respective constant rates, can do the same job in 5 hours. How many hours would it take R, working alone at its constant rate, to do the same job?

A. 8
B. 10
C. 12
D. 15
E. 20

This is my nightmare . I remember studying some formula for combined work in my school days, but forgot. And so everytime , I come across such sums, my brain looks for the formula and fails . Even after trying to work it in RTD method , I am not able to solve. Somebody please help.

Let's assume the work to be something like printing 20 papers. I'm picking 20 as it is the LCM of 4 & 5. Any number in that place will work just as well.

Speed of Three machines together = 5 papers per hour
Speed of Two machines together = 4 papers per hour
So speed of remaining machine = 1 paper per hour

So, to print 20 papers, this machine would take 20/1 = 20 hours. Answer is E.
_________________
Did you find this post helpful?... Please let me know through the Kudos button.

Thanks To The Almighty - My GMAT Debrief

GMAT Reading Comprehension: 7 Most Common Passage Types
##### General Discussion
Manager
Joined: 22 Jun 2005
Posts: 234
Location: London

### Show Tags

04 Mar 2006, 13:44
4
1
1/R+1/S+ 1/T = 1/4
1/S+ 1/T = 1/5
1/R=1/4-1/5
R=20
Manager
Joined: 03 Jan 2015
Posts: 72
Re: Three printing presses, R, S, and T, working together at the  [#permalink]

### Show Tags

23 Dec 2015, 08:50
4
2
$$\frac{1}{r} + \frac{1}{s} + \frac{1}{t} = \frac{1}{4}$$

$$\frac{1}{r} + \frac{1}{s} = \frac{1}{5}$$ $$thus ->$$ $$\frac{1}{5} + \frac{1}{t} = \frac{1}{4}$$

$$\frac{1}{t} = \frac{1}{4} - \frac{1}{5}$$

$$\frac{1}{t} = \frac{5}{20} - \frac{4}{20}$$

$$t = 20$$
Intern
Joined: 27 Nov 2012
Posts: 35
Re: RTD - Combined Worked Sum  [#permalink]

### Show Tags

02 Dec 2012, 13:13
3
1
This is how I solved the problem:
4 hours * (rate of R + rate of S + rate of T) = total job
5 hours * (rate of S + rate of T) = total job

equate the two, reduce them.

4*rate of R = rate of S + rate of T

Plug back into equation 2: 5*(4*rate of R) = total

20* rate of R = total
Director
Joined: 29 Dec 2005
Posts: 931

### Show Tags

04 Mar 2006, 13:35
2
=1/4-1/5=1/20

r can do 1/20 job in 1 hour
r can do the whole job in 20 hours.
Intern
Joined: 08 Jan 2006
Posts: 25

### Show Tags

04 Mar 2006, 13:16
1
vivek123 wrote:
Three printing presses, R, S, and T, working together at their respective constant rates,
can do a certain printing job in 4 hours. S and T, working together at their respective
constant rates, can do the same job in 5 hours. How many hours would it take R, working
alone at its constant rate, to do the same job?
A. 8
B. 10
C. 12
D. 15
E. 20

E.

R, S and T can do Job J in 4 hours. Which also means the in one hour all three will do J/4 th of the job. Also represented by:
1/r+1/s+1/t = j/4

We know that T and S working together do the same job J in 5 hours. Again in 1 hour of T and S working together they will be done with:
1/s + 1/t = J/5

so 1/r + j/5 = j/4
1/r = j/4-j/5=j/20
So in 1 hr working alone R can do 1/20th of J. Therefore R would need 20 hrs.
Manager
Joined: 13 Dec 2005
Posts: 160
Location: Milwaukee,WI

### Show Tags

04 Mar 2006, 18:23
same logic above 1/r =1/5-1/4 ... hence r =20 hrs
Intern
Joined: 27 Aug 2012
Posts: 11
RTD - Combined Worked Sum  [#permalink]

### Show Tags

01 Dec 2012, 01:42
Three printing presses, R, S, and T, working together at their respective constant rates, can do a certain printing job in 4 hours. S and T, working together at their respective constant rates, can do the same job in 5 hours. How many hours would it take R, working alone at its constant rate, to do the same job?

A. 8
B. 10
C. 12
D. 15
E. 20

This is my nightmare . I remember studying some formula for combined work in my school days, but forgot. And so everytime , I come across such sums, my brain looks for the formula and fails . Even after trying to work it in RTD method , I am not able to solve. Somebody please help.
Math Expert
Joined: 02 Sep 2009
Posts: 59236
Re: Three printing presses, R, S, and T, working together at the  [#permalink]

### Show Tags

17 Sep 2013, 07:26
Merging similar topics.
_________________
Manager
Joined: 21 Oct 2013
Posts: 177
Location: Germany
GMAT 1: 660 Q45 V36
GPA: 3.51
Re: Three printing presses, R, S, and T, working together at the  [#permalink]

### Show Tags

20 Nov 2013, 04:56
I did it like this:

rate R: x
rate S: y
rate T: z

We know that work(w) = rate (r) * time
and we can combine rates.

so I did:
R,S,T working together to complete ONE job : 1 = x+y+z *4
S,T working together to complete ONE job: 1 = y+z *5 ==> 1/5 = y+z ==> substitute in first equation I get x = 1/20 which tells me that machine r completes the job in 20h. Hence E.

I took 3 minutes though, because I wasn't 100 % sure that I can solve it like this. Can you please confirm that this is a appropriate way to solve problems like this or explain the answers above a bit more. I think I can follow but not sure.

Thanks!
Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4835
Location: India
GPA: 3.5
Re: Three printing presses, R, S, and T, working together at the  [#permalink]

### Show Tags

06 Dec 2016, 08:29
vivek123 wrote:
Three printing presses, R, S, and T, working together at their respective constant rates, can do a certain printing job in 4 hours. S and T, working together at their respective constant rates, can do the same job in 5 hours. How many hours would it take R, working alone at its constant rate, to do the same job?

A. 8
B. 10
C. 12
D. 15
E. 20

LCM of ( 4, 5 & T ) = 20T

So, let the total work be 20T units...

Combined efficiency of R , S & T is 9+T

Now, 20T/9 + T = 5

Or, 20T = 45 + 5T

So, 15T = 45

Thus, T = 3

So, THe time required by T to do the work will be 20T/T = 20

Hence, correct answer will be (E) 20

_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
Intern
Joined: 25 Feb 2013
Posts: 1
Location: United States
Concentration: Statistics, Economics
GMAT 1: 720 Q47 V42
GPA: 3.5
WE: Other (Commercial Banking)
Re: Three printing presses, R, S, and T, working together at the  [#permalink]

### Show Tags

26 Jan 2017, 09:34
1/5 + 1/x = 1/4

4/20 + 1/x = 5/20

1/x = 1/20

x = 20
Intern
Joined: 28 Apr 2016
Posts: 43
Location: United States
GMAT 1: 780 Q51 V47
GPA: 3.9
Re: Three printing presses, R, S, and T, working together at the  [#permalink]

### Show Tags

20 Oct 2018, 14:28
Even though this is a relatively easy question, it gives us the opportunity to practice a number of my GMAT timing tips (the links below include growing lists of questions that you can use to practice each tip):

Rate problems: Use D = R x T and W = R x T
Like most work rate problems, we can start with the equation W = R x T and then plug in the work, rate, and time for each scenario that we are considering.

Set the amount of work equal to 1 for a single job
Because we’re talking about a single printing job, we just set W = 1 for each scenario.

Add rates when they are simultaneous
Let’s define variables for the rates for printing presses R, S, and T as Rr, Rs, and Rt. Remember that we can add rates when they are simultaneous, so, when all 3 presses are working together, the rate is Rr + Rs + Rt. When just S and R are working together, the rate is Rs + Rt.

Rate and time are reciprocals of each other for a single job
Since we are given the amounts of time for each scenario, we can set the rate equal to the reciprocal of the time for each scenario. This means that Rr + Rs + Rt = 1/4 and Rs + Rt = 1/5. In addition, we are solving for the time it takes printing press R to do the job working alone; if we call this time Tr, then Tr = 1/Rr, and we can solve for Tr if we know Rr.

Eliminate combinations of variables using substitution
While we can’t solve for Rs and Rt separately, we don’t have to. Since we know their sum Rs + Rt = 1/5, we can just plug this value in for (Rs + Rt) in the equation Rr + Rs + Rt = 1/4. This is enough to allow us to solve for Rr, which then allows us to solve for Tr, which is the final answer to this question.

Please let me know if you have any questions, or if you want me to post a video solution!
_________________
Online GMAT tutor with a 780 GMAT score. Harvard graduate.

Manager
Joined: 07 Feb 2017
Posts: 175
Re: Three printing presses, R, S, and T, working together at the  [#permalink]

### Show Tags

20 Oct 2018, 14:40
Solved in 10 seconds without writing
Director
Joined: 19 Oct 2013
Posts: 511
Location: Kuwait
GPA: 3.2
WE: Engineering (Real Estate)
Re: Three printing presses, R, S, and T, working together at the  [#permalink]

### Show Tags

20 Oct 2018, 14:44
vivek123 wrote:
Three printing presses, R, S, and T, working together at their respective constant rates, can do a certain printing job in 4 hours. S and T, working together at their respective constant rates, can do the same job in 5 hours. How many hours would it take R, working alone at its constant rate, to do the same job?

A. 8
B. 10
C. 12
D. 15
E. 20

1/R + 1/S + 1/T = 1/4

We also know 1/S + 1/T = 1/5

So 1/R = 1/4 - 1/5 = 1/20

Time for R = 20

Posted from my mobile device
Intern
Joined: 01 Sep 2011
Posts: 8
Re: Three printing presses, R, S, and T, working together at the  [#permalink]

### Show Tags

26 Oct 2019, 21:36
Assume rate of work of press R, S and T are R, S and T
Given, R+S+T=1/4
S+T=1/5
Then , R=1/4-1/5=1/20
If R can the job's 1/20 part in 1 hour , then can do the whole job in 20 hours.
Ans. 20
Intern
Joined: 19 Sep 2017
Posts: 3
Three printing presses, R, S, and T, working together at the  [#permalink]

### Show Tags

30 Oct 2019, 13:15
TOTAL HOURS (S,T,R)=(S and T)*R/ (S and T) +R
SO, 4=5R/5+R
R=20
ANS:E
Three printing presses, R, S, and T, working together at the   [#permalink] 30 Oct 2019, 13:15
Display posts from previous: Sort by