SOLUTION: A monk starts walking to another town at 7 AM. The path is over a mountain and not straight. He stops at least once to eat. ----------- ---- The next day, he starts walking bac

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Question 1065806: A monk starts walking to another town at 7 AM.
The path is over a mountain and not straight.
He stops at least once to eat.
----------------
The next day, he starts walking back at 7 AM.
He again stops to eat at some time.
======================
Prove (or demonstrate) that he was at the same point at the same time on the 2 days.

Found 2 solutions by ikleyn, Alan3354:
Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.
This story is for kindergarten, not for math forum.

Otherwise, I must re-write this story from scratch to make it as a math problem should be.

Which I DO NOT WANT to do.



Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A monk starts walking to another town at 7 AM.
The path is over a mountain and not straight.
He stops at least once to eat.
----------------
The next day, he starts walking back at 7 AM.
He again stops to eat at some time.
======================
Prove (or demonstrate) that he was at the same point at the same time on the 2 days.
----------------
Graph his distance from the 1st day's starting point, distance vs. time.
The graph of the 2nd day has to intersect the graph of the 1st day.
At that intersection, the time and distance are the same on both days.
So he must be at the same point at the same time the next day.
graph%28300%2C+200%2C+0%2C+55%2C+0%2C+20%2Cx%2C-x%2B20%29
The graph shows straight lines, which would not be the case, but whatever the shape of the lines, they have to intersect.
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PS An interesting problem. It is possible that a kindergartener would "solve" it. Kids have perspectives and insight that most adults lack.