# At 5 AM one day, a monk began a trek from his monastery by the sea to the monastery at the top of a mountain.

At 5 AM one day, a monk began a trek from his monastery by the sea to the monastery atthe top of a mountain. He reached the mountain-top monastery at 11 AM, spent the rest ofthe day in meditation, and then slept the night there. In the morning, at 5 AM, he beganwalking back to the seaside monastery. Though walking downhill should have been faster,he dawdled in the beautiful sunshine, and ending up getting to the seaside monastery atexactly 11 AM.(a) Was there necessarily a time during each trip when the monk was in exactly the sameplace on both days? Why or why no(b) Suppose themonkwalked faster on the second day, and got back at 9 AM.What is youranswer to part (a) in this case?(c) Suppose the monk started later, at 10 AM, and reached the seaside monastery at 3 PM.What is your answer to part (a) in this case?

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