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A running "aha" puzzle



A boy walks out on a train trestle high above a river. He has walked 4/7 of the way across the trestle when he spots a train coming at him head-on. He realizes that he has just enough time either to run toward the train and jump off the trestle or to run away from the train and get off the trestle. If the boy can run 6 miles per hour, how fast is the train moving toward him?

Can you answer without writing anything down?

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If the boy runs toward the train, the train makes a certain distance.

If the boy runs away from the the train, the train makes the same distance plus the bridge.

In the second case, the boy ran 1/7th of the bridge more, the train the whole bridge more. So the train is seven times faster than the boy.
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