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Train A leaves a station traveling at 80 kilometers per hour. 8 hours later, train B leaves the same station traveling in the same direction at 90 kilometers per hour. How long does it take train B to catch up to train A?
One thing to notice about these "catch-up" problems, is that when one catches
up with the other, they will have traveled the same distance, we don't what the
distance is, but we do know that they are the same. We can make a distance
equation from this simple fact.
Let t = time required by Train B to catch up
(t+8) = time when Train A is caught
Distance = speed * time:
90t = 80(t+8)
90t = 80t + 640
90t - 80t = 640
10t = 640
t = 640/10
t = 64 hr for B to catch up with A
Now, we can find out the distances, and by them being equal, we know that our
solutions are correct: Train A time: 64+8 = 72
A: 80 * 72 = 5760 mi
B: 90 * 64 = 5760 also
Did this make sense to you? Any questions?