Two trains, A and B, leave their respective starting points at the same time and travel in opposite directions. They travel at constant speeds, and pass at point M. One travels at twice the speed of the other. If one of the trains leaves five minutes late they pass at a point 2 miles from point M.

What is the speed of the slow train, in miles per hour?

I got 36 miles per hour as the slow train's speed.

If point Z is where they meet when one is late then:


a) If the slow train leaves 5 minutes late, they meet more towards where the slow train was.

Since the fast train has to make up the extra 2 miles from M to Z, the slow train has to be half that distance, or 1 mile from Z when the fast train passes M, Since the slow train is 3 miles from M when it is going 5 minutes late, it must go 3 miles in 1/12 hour, or 36 miles per hour.


b) If the fast train leaves 5 minutes late, they meet more towards where the fast train was.

Using the same reasoning, the slow train makes up the extra 2 miles, so the fast train must be 4 miles from point Z when the slow train is at M. Since the fast train is 6 miles away when it leaves 5 minutes later, it travels 6 miles in 1/12 hour, or 72 miles per hour. This means the slow train moves half this fast, or 36 miles per hour.

These are the same solution, so there is only one solution: The slow train's speed is 36 miles per hour.

Posted by Gamer on 2003-05-10 06:47:58