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Thread: Oh No! It's a Train Puzzle

20030804, 02:46 #1
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Oh No! It's a Train Puzzle
Two men are walking toward each other alongside a railway. A freight train overtakes one of them in 20 seconds and exactly 10 minutes later meets the other man coming in the opposite direction. The train passes this man in 18 seconds. How long after the train has passed the second man will the two men meet? (Constant speeds are to be assumed throughout.) Choo  choo <img src=/S/smile.gif border=0 alt=smile width=15 height=15>
 Ricky

20030804, 07:13 #2
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Re: Oh No! It's a Train Puzzle
<span style="backgroundcolor: #FFFF00; color: #000000; fontweight: bold"><font color=yellow>5562 seconds or 92 minutes and 42 seconds after the train has passed the second man.</font color=yellow></span hi>

20030804, 11:13 #3
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Re: Oh No! It's a Train Puzzle
That's exactly right. At first look, I didn't think there was enough information to resolve... <img src=/S/cheers.gif border=0 alt=cheers width=30 height=16>
 Ricky

20030804, 11:43 #4
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Re: Oh No! It's a Train Puzzle
The fun thing about this puzzle is that you don't know, and don't have to know, the length of the train and the exact speeds of the train and the two men. It's all about proportions.
<span style="backgroundcolor: #FFFF00; color: #000000; fontweight: bold"><font color=yellow>Say that the train is L meters long, and that the speed of the train, first man and second man are V, V1 and V2 meters per second, respectively. (Meters as a unit are unimportant, you can use feet or yards or whatever you prefer).
The train overtakes the first man with a speed of (VV1) meters per second. Since it takes 20 seconds to pass the man, L = 20*(VV1).
The train comes towards the second man with a speed of (V+V2) meters per second. Since it takes 18 seconds to pass him, L = 18*(V+V2).
The two man approach each other at a speed of V1+V2.
From the equations above, it is easy to derive VV1 = L/20, so V1 = VL/20 and V+V2 = L/18, so V2=L/18V. Hence V1+V2 = L/18  L/20 = 10*L/180  9*L/180 = L/180.
The train has completely passed the second man 20 + 10*60 + 18 = 638 seconds after it starts to overtake the first man.
The first man has walked 638*V1 meters by then.
The front of the train has traveled 638*V meters, so second man and the rear of the train are 638*VL meters from the starting point. So the men have to walk 638*VL  638*V1 meters = 638*(VV1)  L = 638/20 * L  L = 30.9*L. Note that all speeds have dropped out of this equation. Since the men approach each other with a speed of L/180 meters per second, this takes 30.9*180 = 5562 seconds. This is independent of the length of the train!</font color=yellow></span hi>