perplexus.info :: Logic : Light at the end of the tunnel

Light at the end of the tunnel (Posted on 2002-05-26)

A man was walking through a tunnel. He is 1/4 of the way through when he hears a train approaching the tunnel from behind him.

If he turns and runs back, he will make it out of the tunnel just as the train is entering it (and will save himself by a hair). If he goes forward to the far end of the tunnel, he will also just barely make it, emerging from the tunnel just as the train is about to catch up to him.

If the man's running speed is 7 miles per hour, how fast is the train moving?

(from techInterview.org)

Submitted by levik

Rating: 3.5000 (14 votes)

Solution: (Hide)

If the man were to start running back, he would have to run 1/4 the length of the tunnel, and reach the start of the tunnel just as the train is entering it.
Since he would run at the same speed either way, he could also run forward, and by the time he ran the same 1/4 of the tunnel, the train would still be just entering it. At this point, the person is at the half-way point of the tunnel, having started 1/4 of the way in, and ran 1/4 more.
Now in the time it will take the man to reach the far end of the tunnel, the train will catch up to him. Therefore, the man will have run 1/2 of the tunnels length in the same period of time that the train covered its entirety. Therefore, the train's speed is twice that of the man, or 14 miles per hour.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Puzzle Solution	K Sengupta	2008-11-18 23:57:34
Answer	K Sengupta	2008-11-17 23:50:33
Solution	salil	2006-02-25 12:13:01
Algebraic Solution	lmnop	2005-01-17 22:24:45
Solution... I think	Lewis	2003-06-03 06:26:20
re: re: Kind of answer	Dulanjana	2002-06-02 06:54:49
re: Kind of answer	levik	2002-05-31 23:09:35
Kind of answer	Dulanjana	2002-05-29 06:07:41
answer?	orlando	2002-05-28 07:35:32
1/2 * X = 1... X=2	Carey	2002-05-27 23:13:20
Solution	Andrew	2002-05-26 16:04:42
Straight Question and Answer	TomM	2002-05-26 15:36:03

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