Solution to Man-Trestle-Train

PROBLEM:

A man is 3/8 of the way walking across a railroad trestle when he hears a train approaching at 60 mi/hr. If he runs to either end of the bridge, he can just make it to safety as the train passes. How fast does he have to run?

SOLUTION:

If he runs back to the near end, he runs 3/8 of a bridge and gets out of the way as the train begins crossing the trestle.

If he runs to the far end, he runs an additional 3/8 of the bridge and is 6/8 (or 3/4) of the way across as the train begins crossing the trestle. He has 1/4 of the way to go while the train has to cross the entire bridge. Therefore he has to run at least at 1/4 of the speed of the train, or 15 mi/hr.