The rate at which water flows out of a pipe, in gallons per hour, is given by a differentiable function $R$ of time $t$. The table below shows the rate as measured every 3 hours for a 24-hour period.

\begin{center}
\begin{tabular}{ c | c }
\begin{tabular}{ c }
$t$ \\
(hours) \\
\end{tabular} & \begin{tabular}{ c }
$R(t)$ \\
(gallons per hour) \\
\end{tabular} \\
\hline
0 & 9.6 \\
3 & 10.4 \\
6 & 10.8 \\
9 & 11.2 \\
12 & 11.4 \\
15 & 11.3 \\
18 & 10.7 \\
21 & 10.2 \\
24 & 9.6 \\
\end{tabular}
\end{center}

(a) Use a midpoint Riemann sum with 4 subdivisions of equal length to approximate $\int_{0}^{24} R(t)\, dt$. Using correct units, explain the meaning of your answer in terms of water flow.

(b) Is there some time $t$, $0 < t < 24$, such that $R'(t) = 0$? Justify your answer.

(c) The rate of water flow $R(t)$ can be approximated by $Q(t) = \frac{1}{79}\left(768 + 23t - t^2\right)$. Use $Q(t)$ to approximate the average rate of water flow during the 24-hour time period. Indicate units of measure.