Question 287827: A man leaves point A at 8 am and arrives in point B at 8pm. The next day he leaves point B at 8am and arrives in point A at 8 pm. Question: is there a location anywhere between points A and B that he passed at exactly the same time, regardless of any fluctuations of speed in his journey? If so, how can it be proved?
Answer by richwmiller(17219)   (Show Source):
You can put this solution on YOUR website! The logical point to consider is the midway point.
But since there might be a fluctuation in speed, you can't be certain of that either. On the A to B trip he might go faster at the beginning so arrive at the halfway point at noon. On the return trip he might go steady and arrive at the half way point at 2 pm.
Student responded:
But does not it stand to reason that if two people do the trip, one from point A to B, the other from B to A, both bound to leave at 8am and arrive at 8pm, will cross paths at some point, regardless of speed? thus if one person does the trip twice, the same would happen?
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