Chapter 6.1, Problem 66E

Two runners At noon (t = 0), Alicia starts running along a long straight road at 4 mi/hr. Her velocity decreases according to the function v(t) = 4/(t + 1), for t ≥ 0. At noon, Boris also starts running along the same road with a 2-mi head start on Alicia; his velocity is given by u(t) = 2/(t + 1), for t ≥ 0. Assume t is measured in hours.

1. a. Find the position functions for Alicia and Boris, where s = 0 corresponds to Alicia’s starting point.
2. b. When, if ever, does Alicia overtake Boris?