Tom and Sue took a bike ride, both starting at the same time and position. Tom started riding at 20 mi/hr, and his velocity decreased according to the function v(t) = 20e^-2t for t ≥ 0. Sue started riding at 15 mi/hr, and her velocity decreased according to the function u(t) = 15e^-t for t ≥ 0.

a. Find and graph the position functions of Tom and Sue.

b. Find the times at which the riders had the same position at the same time.

c. Who ultimately took the lead and remained in the lead?