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?
(In reply to
preliminary thoughts by Steven Lord)
Statement 2) "The tunnel length need not be an integer number of meters, since the car and 1st man, although traveling at integer rates from either end, do not necessarily meet on an integer minute"
The problem specifies that the engineers each walk at an "integer speed", and they all enter/exit the car at an "integral number of minutes" with "no pauses". So, shouldn't the first man encounter the car at some integer number of minutes? And wouldn't this then force the tunnel to be an integer length?
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Posted by Kenny M
on 2019-04-21 09:01:38 |
re: preliminary thoughts - are you sure?
