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Tunneling through a mine car (Posted on 2019-04-16) Difficulty: 3 of 5
Four safety engineers set out to inspect a newly cut tunnel through Mt. Popocaterpillar in the Andes. Each person walks at a different constant integer speed measured in meters per minute. In the tunnel there is a mine car which travels along a fixed track, automatically going from end to end at a fixed integer speed. When people board the car they may reverse its direction, but cannot change its speed.

At noon on Monday all four engineers start at the south end, while the mine car starts at the north end. The first (fastest) engineer meets the car, and takes it some distance north. The engineer gets out and continues going north, while the car resumes heading south. Then the second engineer meets the car and also takes it some distance north. Likewise for the third and fourth engineers. All the people, and the mine car, travel continuously with no pauses. The inspectors always go north. Each person enters and exits the car at an integral number of minutes.

All four engineers reach the end of the tunnel simultaneously. What is the earliest time this could happen?

No Solution Yet Submitted by Danish Ahmed Khan    
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  Subject Author Date
Yes - my solution is in error - thanksSteven Lord2020-07-22 08:45:19
just an aside Steven Lord2020-07-21 20:17:03
Butarmando2020-07-21 15:30:07
re(2): Solution (but hidden...)armando2020-07-21 12:08:50
re: Solution (but hidden...)Steven Lord2020-07-21 11:32:16
Solution (but hidden...)armando2020-07-20 16:09:57
New lower limit and new 3 person solutionSteve Herman2019-04-26 12:47:34
re(3): solnSteve Herman2019-04-26 12:08:48
re(2): solnSteven Lord2019-04-25 19:01:19
re: solnSteve Herman2019-04-25 15:51:32
solnSteven Lord2019-04-24 21:40:38
Hints/TipsThe two person case (supporting calculations)Steve Herman2019-04-23 13:14:23
Hints/TipsThe two person case (corrected)Steve Herman2019-04-23 09:52:46
Level of Difficulty Kenny M2019-04-23 09:17:38
re(2): The two person caseSteve Herman2019-04-23 08:59:34
re: The two person caseKenny M2019-04-22 22:43:52
re: The two person caseSteven Lord2019-04-22 22:26:29
Some ThoughtsThe two person caseSteve Herman2019-04-22 18:30:29
two more corrections to my ideasSteven Lord2019-04-22 00:48:38
re(3): preliminary thoughts - are you sure?Kenny M2019-04-21 20:13:15
re(2): preliminary thoughts - are you sure?Steven Lord2019-04-21 09:54:15
re: preliminary thoughts - are you sure?Kenny M2019-04-21 09:01:38
preliminary thoughtsSteven Lord2019-04-21 04:38:43
No Subjectarmando2019-04-20 10:47:34
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