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
re(2): soln by Steven Lord)
Steven Lord,
You muse: I wonder if there is a single best solution if the parameters allowed the freedom to be nonphysical.
My answer: Of course there is a best answer if allowed the freedom to be non-physical, because the answer is an integer. You have established an upper limit on the minimum of 34 (corresponding to travel times of 1,2,4 and 10). One obvious lower limit is 20 (corresponding to travel times of 1,2,3 and 4). So the best answer is between 20 and 34 (inclusive).
re(3): soln
