# Runners

If John has a running speed of 3.5miles per hour and Lucy has a speed of 5 miles per hour. If John starts running at 10:00 am and Lucy starts running at 10:30 am, at what time will they meet? (as soon as possible)

Result

t = 11:40 hh:mm

#### Solution:

$v_{1}=3.5 \ \text{mph} \ \\ v_{2}=5 \ \text{mph} \ \\ t_{2}=10+30/60=\dfrac{ 21 }{ 2 }=10.5 \ \text{h} \ \\ \ \\ s_{1}=s_{2} \ \\ \ \\ v_{1} \cdot \ (t-10.00)=v_{2} \cdot \ (t-t_{2}) \ \\ \ \\ 3.5 \cdot \ (t-10.00)=5 \cdot \ (t-10.5) \ \\ \ \\ 1.5t=17.5 \ \\ \ \\ t=\dfrac{ 35 }{ 3 } \doteq 11.666667 \ \\ =11.66667 \doteq 11:40 \ \text{hh}:\text{mm}$

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