A Man Walking on Railroad Bridge

A man is walking across a railroad bridge that goes from point A to point B. He starts at point A, and when he is 3/8 of the way across the bridge, he hears a train approaching. The train's speed is 60 mph (miles per hour). The man can run fast enough so that if he turns and runs back toward point A, he will meet the train at A, and if he runs forward toward point B, the train will overtake him at B.

How fast can the man run?


He must be running at 'this' speed! 

Speed Needed For Run on Bridge

Why to calculate the speed?

If the man turns back and runs towards A for 3/8 of distance while train reaches at the point A. That means the train train reaches at point A when man runs for 3/8 distance.

So if man continues to run towards point B then, while he covers 3/8 distance the train reaches at point A. Now, man is 3/8 + 3/8 = 6/8 = 3/4 distance away from the point A where B is 1/4 away from him now.

Again, we know, the train will overtake the man at point B covering total distance between A and B. Till then man can run only 1/4 th distance between A and B to reach B.That mean the train must be 4 times faster than the speed of man.

Since, train is traveling at 60 mph, the speed of man = (1/4)x60 = 15 mph.