For several weeks, the highway department has been recording the speed of freeway traffic flowing past a certain downtown exit. The data suggest that between the hours of 1:00 and 6:00 P.M. on a normal weekday, the speed of traffic at the exit is approximately S(t) = t³ − 10.5t² + 30t + 20 miles per hour, where t is the number of hours past noon.

a. Compute the average speed of the traffic between the hours of 1:00 and 6:00 P.M.

b. At what time between 1:00 and 6:00 P.M. is the traffic speed at the exit the same as the average speed found in part (a)?