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A man needs to go through a train tunnel. He starts through the tunnel and when he gets 1/4 the way through the tunnel, he hears the train whistle behind him. you don’t know how far away the train is, or how fast it is going, (or how fast he is going).  All you know is:

1. if the man turns around and runs back the way he came, he will just barely make it out of the tunnel alive before the train hits him.
2. if the man keeps running through the tunnel, he will also just barely make it out of the tunnel alive before the train hits him.

Assume the man runs the same speed whether he goes back to the start or continues on through the tunnel.  Also assume that he accelerates to his top speed instantaneously.  Assume the train misses him by an infintisimal amount and all those other reasonable assumptions that go along with puzzles like this so that some wanker doesn’t say the problem isn’t well defined.

How fast is the train going compared to the man?

### Solution

I haven’t written up a solution for this yet, but smarter people than I have described some on the discussion forum. You can read their thoughts here.