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Two boys train escape puzzle

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Two 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?

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SherlockHolmes Expert Asked on 25th November 2015 in Math Puzzles.
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    • 1 Answer(s)

    Speed of the train – 30 miles per hour

    Explanation:
    Its a hint- 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 hint line to be true.
    Hence,
    Train will run 3 times faster then B
    and B is running at 10miles per hour so, train will run at 30 miles per hour.

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    Detective Expert Answered on 27th November 2015.
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