A strong west wind blows across a circular running track. Abe and Bess start running at the south end of the track, and at the same time, Abe starts running clockwise and Bess starts running counterclockwise. Abe runs with a speed (in units of mi/hr) given by u(φ) = 3 - 2 cos φ and Bess runs with a speed given by v(θ) = 3 + 2 cos θ, where φ and θ are the central angles of the runners.

a. Graph the speed functions u and v, and explain why they describe the runners’ speeds (in light of the wind).

b. Compute the average value of u and v with respect to the central angle.

c. Challenge: If the track has a radius of 1/10 mi, how long does it take each runner to complete one lap and who wins the race?

Abe Bess wind start