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Answer to railroad bridge

The train is twice as fast as the man.

If the man continues down the bridge: when he gets to the 1/2 way mark the train will be at the start of the bridge.

(This is becasuse if the man went back the beginning of the bridge, 1/4 of the way, the train would meet him there.  So if he continues 1/4 more of the way down the bridge to the 1/2 mark, the train will still be moving and be at the beginning of the bridge)

So we know the train and the man will reach the end of the bridge at the same time.  The man has 1/2 of the bridge to cross and the train has the whole bridge to cross.
So.... the train must be doing twice the speed of the man!

Julian Hall
Wednesday, November 20, 2002

The person has crossed 1/4 th distance of the tunnel length. It means he divides the tunnel into the ratio of 1:3.  Let us say tunnel length is 4 unit distance.

Time taken to reach his starting point is less than time taken to reach other end of the tunnel. From the given statements the train is coming towards his starting point.

Let us say train should cover x unit distance to reach his starting point.  The train should cover x+4 unit distance to reach other end of tunnel.

Let man's speed is M
Let train's speed is T

Time taken by train to reach the starting point = Time taken by the man to reach his  starting point

x / T = 1 / M  --------- Eqn 1

Time taken by train to reach other end of tunnel = time taken by the man's to reach other end of tunnel.

(4+x) / T = 3 / M --------------- Eqn 2

Solve the Eqn 1 and Eqn 2

Mx = T
Mx + 4M = 3T
4M = 2T
T = 4M / 2 = 2M

Hence Train speed = 2 * Man's speed.

Monday, November 25, 2002

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