Question

Two trains leave stations 238 miles apart at the same time and travel toward each other. One train travels at 75 miles per hour while the other train travels at 95 miles per hour. How long will it take for the two trains to meet?

Answer 1

Say the first train starts from x=0, and moves to the right (+x-direction), at 95 mph. The distance covered by the train can be given by x = 95*t (where t is the time in hours).

Then, the other train is moving in the opposite direction (-x-direction), at 75 mph. The distance covered by that train can be given by x = -75*t + 238 (since the second train starts 238 miles from the first)

The two trains meet at the intersection of these two equations. We want to know when the trains meet, so we can solve for t right away and eliminate x:

x = 95t

x = -75t + 238

--> 95t = -75t + 238

170t = 238

t = 1.4

The trains will meet after 1.4 hours (or 1 hour and 24 minutes).

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