# Puzzle: How fast train was going?

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Suppose 2 boys are walking in the woods and they decide to take a shortcut through a railroad tunnel. They had walked 2/3 of the way through the tunnel, but then something horrible happened: a train was coming in the opposite direction towards the 2 boys, and it was coming close to the other entrance of the tunnel. Each boy ran in a different direction to get out of the tunnel and avoid the incoming train. Each boy ran at the same exact speed of 10 miles per hour, and each boy managed to escape the train at the exact instant in which the train would have hit and killed him. If the train was moving at a constant speed and each boy was capable of instantaneous acceleration, then how fast was the train going?

posted Jan 18, 2014

+1 vote

30 miles per hour is the speed of the train.

Logic: use below line as clue
each boy managed to escape the train at the exact instant in which the train would have hit and killed him

let A is running toward the train and B is moving in opposite direction.
So the distance which A has to cover=1-2/3=1/3
the distance which B has to cover=2/3
and speed of A and B is same hence A and B will cover the same distance 1/3,
A just escaped when train is at the entrance of the tunnel hence remaining distance for B is 2/3-1/3=1/3

Now B will cover 1/3 and train will cover 2/3 for the clue line to be true
hence train will run 3 times faster then B

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