Answer
a) -2000 gal/min.
b) -2500 gal/min.
Work Step by Step
a) We take the derivative of $W$ to find the rate:
$W'(t) = 100 * 2 * (t-15)$
$W'(5) = 200* (5-15) = -2000$ gal/min.
b) The average rate of water flow is equal to $\frac{W(5)-W(0)}{5-0} = \frac{100(5-15)^2- 100(0-15)^2}{5-0}=-2500$ gal/min.
