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?