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I am having trouble solving this problem. In particular I am having difficulty translating this problem into an equation.

Question:

A train leaves a station and travels east at 75 km/h. Two and a half hours later, a second train leaves the same station on a parallel track travelling east at 125 km/h. How far from the station will the second train overtake the first train?

I believe that when the second train leaves, the first train is $187.5$ km from the station:

$75\times2.5 = 187.5$

By the time the second train gets to the position of where the first train was when it (second train) left, the first train will have moved for another 1.5 hours:

$187.5\div125=1.5$

The first train would now be $300km$ away from the station.

$75\times1.5=112.5$

$112.5+187.5=300$

I am honestly just having trouble thinking through this problem. I also think that the way I am currently thinking about solving this is either incorrect or more complicated than needed.

If anyone could point me in the right direction that would be greatly appreciated.

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The second train travels 50 kph faster than the first train. Each hour, the distance between the two trains closes by 50 km. To catch up a total distance of 187.5 km at a rate of 50 km/h...

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  • $\begingroup$ +1. Thank you for your answer. That made this problem very simple. $\endgroup$ – user161695 Dec 14 '14 at 2:33

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