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?
Steven. In my last post some hours ago, I made a quick check with your 46 minutes time solution and it seems all right. But looking with some more detail there is something I'm not understanding.
From your 46 minutes solution
Tunnel 1:
Length: 2310 m, Time: 46 minutes: car speed: 105 m/min
Walking speeds: 49, 45, 45, 42, 35. E1 1st walk 15 min,
Car times 1, 4, 6, 10, min
The first engineer walks for 15 minutes at speed 49. He has walked then 735 meters. After that he enters the minecar for 1 minute at speed 105, leaves the car and the car goes back for at least other minute, and then the second engineer takes it.
At that point the minecar is again at 735 meters from the start and the time from the beginning is 17 minutes.
But that implies that the speed of the second engineer is 735/17= 43.235 meters/min instead of 45 meters/minute.
I'm not sure you have accorded the speed of the engineers with the path and time of the minecar (the engineers board the minecar at an integral number number of minutes).
Or perhaps I'm not seeing something?
Edited on July 21, 2020, 3:36 pm
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Posted by armando
on 2020-07-21 15:30:07 |
But
