Chapter 5.6, Problem 69ES

(a) Suppose that a reservoir supplies water to an industrial park at a constant rate of $r=4$ gallons per minute (gal/min) between $8:30\text{ A}\text{.M}\text{.}$ and $9:00\text{ A}\text{.M}$ . How much water does the reservoir supply during that time period?

(b) Suppose that one of the industrial plants increases its water consumption between $9:00\text{ A}\text{.M}$ and $10:00\text{ A}\text{.M}\text{.}$ and that the rate at which the reservoir supplies water increases linearly, as shown in the accompanying figure. How much water does the reservoir supply during that $1\text{-hour}$ time period?

(c) Suppose that from $10:00\text{ A}\text{.M}\text{.}$ to $12$ noon the rate at which the reservoir supplies water is given by the formula $r\left(t\right)=10+\sqrt{t}\text{ gal/min}$ , where $t$ is the time (in minutes) since $10:00\text{ A}\text{.M}\text{.}$ How much water does the reservoir supply during that $2\text{-hour}$ time period?