For several weeks, the highway department has been recording the speed of freewa

Question

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)= t^3 - 10.5t^2 + 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)?

Explanation / Answer

S(t)= t^3 - 10.5t^2 + 30t + 20 miles per hour
Integrate above wrt t and put limits( 1 to 6) =193.75
a) 196.25 / 5 = 39.25 miles/hour
b) 39.25 =t^3 - 10.5t^2 + 30t + 20
t = 0.9 hours and 3.5 hours

(b) At times 01:54 and 04:30, speed of exit is same as average

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