At 5 AM one day, monk starrted the trek from the monastery by sea to monastery at the top of the mountain. He reached mountain-top monastery at 11 AM, spent rest of day in meditation, and then slept night there. In morning, at 5 AM, he started walking back to seaside monastery. Although walking downhill must have been faster, he dawdled in beautiful sunshine, and ending up getting to seaside monastery at exactly 11 AM.
(a) Was there essentially a time during each trip when monk was in exactly same place on both days? Why or why not?
(b) Assume monk walked faster on second day, and got back at 9 AM. What is the answer to part (a) in this case?
(c) Assume monk started later, at 10 AM, and reached seaside monastery at 3 PM. What is the answer to part (a) in this case?