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# Escaping the train

## Question

A man walking home takes a shortcut through a train tunnel. A quarter of the way in, he hears a train whistle behind him. The tunnel is not wide enough for the man to escape being hit by the train, so he must either turn back, or go forward, at his top speed of 20 mph. Either way he will escape, but by the slimmest of margins. How fast is the train moving?

All correct solutions will be accepted.

The coveted bonanova Gold Star will be awarded for a solution that can be explained in words only, without equations or algebra. (e.g. without saying, "Let T be the speed of the train and D be the distance of the train from the tunnel, then t = D/T is the time that the man has in order to ..." etc. )

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The train is travelling at 40mph. If the man can escape either way then he can cover ¼ the distance of the tunnel by the time the train reaches the entrance to the tunnel. If running in the other direction he will thus be half way through the tunnel by the time the train reaches the entrance. Since he only escaped by the slimmest of margins,  the train effectively reaches the end of the tunnel at the same time, and hence travelled the entire length of the tunnel in the time it took the man to travel half the length of the tunnel. So the train is travelling at twice the speed of the man.

Edited by bonanova
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Spoiler

ratio 4:3

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On 6/26/2016 at 4:51 PM, Charlie said:

The train is travelling at 40mph. If the man can escape either way then he can cover ¼ the distance of the tunnel by the time the train reaches the entrance to the tunnel. If running in the other direction he will thus be half way through the tunnel by the time the train reaches the entrance. Since he only escaped by the slimmest of margins,  the train effectively reaches the end of the tunnel at the same time, and hence travelled the entire length of the tunnel in the time it took the man to travel half the length of the tunnel. So the train is travelling at twice the speed of the man.

Hello Charlie ..i got it wrong! I guess you are right graphically.

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I like Charlie's argument; I think Charlie earns the BGS,

Edited by CaptainEd
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On 6/29/2016 at 11:55 AM, CaptainEd said:

I like Charlie's argument; I think Charlie earns the BGS,

I agree. I put it into his post.

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