Rate-Time-Distance Word Problems

Or otherwise known as those dreaded train problems. These are always tricky for algebra students. Ask someone you know which problems they remember from Algebra I and almost all of them will have something to say about the train problems.

Train problems can be separated into two categories: same direction travel and opposite direction travel. Each are handled differently, but using a chart makes it easier to set up the equations. You also have to remember that distance equals rate times time or d=rt.

Here is an example. A train leaves the train station at 2:00 p.m. Its average rate of speed is 90 mph. Another train leaves the same station a half hour later. Its average rate of speed is 120 mph. If the second train follows the same route on a parallel track to the first, how many hours will it take the second train to catch the first?

Train	Rate	Time	Distance
1	90	t	90t
2	120	t-0.5	120(t-0.5)

Since the trains are travelling in the same direction, their distances are equal when the 2nd one catches the 1st. Therefore, to solve this equation, we set the distance of Train 1 equal to Train 2.

90t = 120(t-0.5)
90t = 120t - 60
-30t = -60
t = 2

The first train travelled for 2 hours before the 2nd train caught up to it. The problem asks how long it takes the 2nd train to catch the first. So it takes the 2nd train a half hour less than it did the first train which is 1.5 hours.

Check back tomorrow for information on opposite direction travel.