Déjà Vu At 8:00 a.m. on Saturday, a man begins running up the side of a mountain to his weekend campsite (see figure). On Sunday morning at 8:00 a.m., he runs back down the mountain. It takes him 20 minutes to run up but only 10 minutes to run down. At some point on the way down, he realizes that he passed the same place at exactly the same time on Saturday. Prove that he is correct. [Hint: Let s(t) and r(t) be the position functions for the runs up and down, and apply the Intermediate Value Theorem to the function .]
