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.

The train is twice fast going relative to the man.

Step-by-step explanation:

Consider the provided information.

Let the distance between the train and beginning of bridge is x and length of bridge is y.

A man is on a 1/4 on a bridge. Thus, the 1/4 of y is y/4.

The train is going x distance in time man runs y/4 distance.

Also if the train is going x + y in time man runs the distance 3y/4.

For better understanding refer the figure 1:

So, if train goes x+y-x distance in time man covers the distance 3y/4 - y/4

Now solve 3y/4 - y/4 = 2y/4

The train covers y distance in the time man runs 2y/4 = y/2

That means train covers 2 times of the distance cover by the man or the train goes twice as fast as man.

Hence, train is twice fast going relative to the man.