Question

11) A man is on a 1/4 on a bridge. A train is coming the same direction he is going. The man can run across the bridge in the same direction and make in barely in time. He can also run backwards towards the train and also barely make it. How fast is the train going relative to the man?

Answer 1

15mph

If the man turns and runs toward point A, he will cover

3/8 of the length of the bridge in the time that it takes

the train to reach A.

If the man runs forward toward point B, what part of the bridge

will he cover before the train reaches A? Well, he will cover

3/8 of the bridge, only heading forward toward B. This will put

him 3/8 + 3/8 = 6/8 = 3/4 of the way across the bridge by the

time the train reaches A.

since we know that the man and the train will meet at B, this

means that in the time it takes the man to run the remaining

1/4 of the bridge, the train will cover the entire length of

the bridge.

If it takes the man the same time to cover 1/4 of the bridge

that it takes the train to cover the whole bridge, then the train

must be going four times as fast as the man. Another way of saying

this is that the man runs at 1/4 the speed of the train.  

Since the train's speed is known to be 60 mph, this means that

the man runs at (1/4) 60 = 15 mph.