Math CentralQuandaries & Queries


Question from chris, a student:

Train A passes a station at 3:15am going 40mph. Train B passes the same station at 3:27am going 50mph. At what time will Train B catch up with Train A?

Hi Chris.

Let's use T to represent the number of hours between the time train B leaves the station and the time it catches up to train A.

Then train B goes 50 x T miles, right? When you multiply the speed by the time, you get the distance.

Now remember that train A had a 12 minute head start. That's 0.2 hours. So train A has travelled at 40 mph for T + 0.2 hours. So its distance traveled from the station is 40 x (T + 0.2).

But haven't both trains gone the same distance?

You should be able to form an equation and find the value of T.

Hope this helps,
Stephen La Rocque

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