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
Solution (but hidden...) by armando)
A,
Hmmm. I thought I had this one, and so I will double check my work and lay out my (2) solutions in a manner that allows for easy self-consistency checks. Rather than play hidden numbers, I hope you will take a look (when I get it done :-) and make sure we each have used the same assumptions, agree on the sequence of events, and yet have still arrived at different answers for E1 walk duration, car and E travel speeds, and tunnel length so as to minimize total time. Cheers, S
re: Solution (but hidden...)
