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
But by armando)
Armando:
This is how I see my result is in error:
I state E1 walks at 49 m/min, and walks first for 15 min and then takes the car for 1 min. The car goes 105 m/min.
E2 walks at 45 m/min.
This leads to problems.
By 16 mins E1 and the car are at distance 840 m because E1 has traveled 735 m by foot and 105 m more in the car.
Now at 16 minutes, E2 has walked to distance 720. So E2 and the car are now 120 m apart and headed toward each other. If another 1 min goes by, they pass each other by!
Also - I am reviewing my assumption that each of the Engineers 2, 3, 4 had walking speeds in that order: s2>s3>s4. I am now not convinced that this is necessary. The problem only states E1 is the fastest and that they all walk at different speeds.
Also note: while all speeds and car step-ons and steps-offs occur at integer minute, nowhere does the problem state that the four arrive at the end of the tunnel on an integer minute.
Neither is it stated that the car must go faster than the Inspectors!
One could imagine fast hikers taking a short slower car ride.
The last inspector need not walk after the car, although a case like this would then force the total time to be integer.
More to come.
S
Edited on August 4, 2020, 3:36 am
Yes - my solution is in error - thanks
