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: v_T(t) = 10, for t ≥ 0 

Sasha: v_S(t) = 15t, for 0 ≤ t ≤ 1 and v_S(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?