MATHEMATICS · Multi-part · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change
Problem
During an eight–hour pumping test, the instantaneous flow rate of water, measured in gallons per hour, was recorded as a function of time t (in hours) by
r(t)=⎩⎨⎧20t,80,160−20t,0≤t≤2,2<t≤5,5<t≤8.
Answer the following questions about the pumping operation on the interval 0≤t≤8.
(1) Part 1: (a) Compute the average flow rate during the entire eight–hour period.
(2) Part 2: (b) Determine all times t in the interval [0,8] at which the instantaneous flow rate equals the average flow rate found in part (a).
(3) Part 3: (c) Interpret the meaning of the average flow rate in the context of this pumping test.