If a cylindrical tank holds 140000 gallons of water, which can be drained from the bottom of the tank in an hour, then Torricelli's Law gives the volume $V$ of water remaining in the tank after $t$ minutes as $$V(t) = 140000\left(1 - \frac{t}{60}\right)^2, \qquad 0 \leq t \leq 60$$

(a) Find the rate at which the water is flowing out of the tank (the instantaneous rate of change of $V$ with respect to $t$) as a function of $t$.

Rate of Flow =

(b) Find both the flow rate and the amount of water remaining in the tank for the times given below.

(i) $t = 0$:

Flow rate = Amount of water remaining =

(ii) $t = 10$:

Flow rate = Amount of water remaining =

(iii) $t = 20$:

Flow rate = Amount of water remaining =

(iv) $t = 30$:

Flow rate = Amount of water remaining =

(v) $t = 40$:

Flow rate = Amount of water remaining =

(c) At what time is the flow rate the greatest?

$t$ =

At what time is the flow rate the least?

$t$ =