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: soln by Steve Herman)
Thanks, Steve.
Actually the best was 34 mins. (I had forgotten)
Here is the 34 min madness -but I agree with you about engineers :-)
Tunnel 4 Under Mt. Popocaterpiller:
Time: 34 min
Length 54,720 m
E1 walks 9 min
mine car travels at 4560 m/s (180 mph)
E (assisted) walking speeds: 1520 (60 mph!), 1425, 1216, 380 m/min
Time in car: 1, 2, 4, 10 min
As for out-of-scope results like this - there may be more. This
case (walking faster than 28 mph) came out due to a bug I had that didn't limit the E1 speed correctly. I only searched exhaustively within the range I specified. (Yes - as a purely numbers problem, there are likely shorter times somewhere way out there. But I needed a limit simply to get a conclusion).
Steve
PS - I am guessing the "answer in the queue" shows a relationship between the variables such that ratios resolve to integers and those integers when added to the num. and denom.s of other ratios also resolve to integers (distances and times). I wonder if there is a single best solution if the parameters allowed the freedom to be nonphysical.
Edited on July 20, 2020, 8:50 pm
re(2): soln
