Chapter 5.4, Problem 23MS

Take a hike (ExH). A hiker decides to climb up Mount Sanitas. There is only one trail to the top, lie starts at the base of the mountain at 8:00 A.M. Saturday. He climbs, stops, rests, backtracks a hit, but finally gets to the summit by 5:00 P.M. that evening. The next morning at 8:00 a.m. he begins to hike down. Again he stops, rests, backtracks (in fact returns back to the top because he left his tent up there), but finally gets back to the bottom by 5:00 p.m. that evening. Must there exist a precise point (altitude) on the trail with the property that, at the very moment he crossed that point, his watch showed the exact same time going up as it did coming down? Carefully explain your answer.