Brianna M.

asked • 09/16/16# A passenger train leaves a train depot 2 h after a freight train leaves the same depot.

The freight train is traveling 18 mph slower than the passenger train. Find the rate of each train if the passenger train overtakes the freight train in 3 h.

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## 1 Expert Answer

So, Brianna, let's look at what we have. Distance = rate x time, right?

If we say p = the passenger train's rate, then it's gone 3p miles when it overtakes the freight train.

The freight train has been travelling for 5 hours at 18 mph slower, so it's gone 5(p - 18) = 5p - 90 miles.

If they are meeting, then they have both travelled the same distance!

3p = 5p - 90

2p = 90

p = 45

This means that the passenger train was travelling at 45 mph and the freight train at 45 - 18 = 27 mph.

Let's check. In 5 hours, the freight train travelled 5(27) = 135 miles. The passenger train travelled 3(45) = 135 miles. Check!

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Nathan B.

09/16/16