Theo and Sasha start at the same place on a straight road, riding bikes with the following velocities (measured in mi/hr).

Assume t is measured in hours. Theo: vT(t)44=10. for t≥0. Sasha: vs(t)=15 t, for 0≤t≤1 and vs(t)=15, for t>1.

a. Graph the velocity functions for both riders.

b. If the riders ride for 1 hr, who rides farther? Interpret your answer geometrically using the graphs of part (a).

c. If the riders ride for 2 hr, who rides farther? Interpret your answer geometrically using the graphs of part (a).

d. Which rider arrives first at the 10-, 15-, and 20-mile markers of the race? Interpret your answer geometrically using the graphs of part (a).

e. Suppose Sasha gives Theo a head start of 0.2 mi and the riders ride for 20 mi. Who wins the race?

f. Suppose Sasha gives Theo a head start of 0.2 hr and the riders ride for 20 mi. Who wins the race?