The rectangular cistern $($storage tank for rainwater$)$ shown has its top $10$ ft below ground level. The cistern, currently full, is to be emptied for inspection by pumping its contents to ground level. Assume that the water weighs $62\mathrm{.}4l\frac{b}{t^3}.$

Complete parts a$.$ through d$.$ below.

a$.$ How much work will it take the empty the cistern? Set up an integral to find the work done.

$W={\displaystyle \underset{15}{\overset{18}{}}}62\mathrm{.}4(234y)dy$

How much work does it take to empty the tank?

$$

$($Round to the nearest integer as needed.$)$

b$.$ How long will it take a $\frac{1}{2}-$hp pump, rated at $275$ ft $-$b$/$sec to pump the tank dry?

$44$ minutes $($Round to the nearest integer as needed.$)$

c$.$ How long will it take the pump in part $b.$ to empty the tank halfway? $($It will be less than half the time required to empty the tank completely.$)$

minutes $($Round to the nearest integer as needed.$)$

d$.$ What are the answers to parts a$.$ through c$.$ in a location where water weighs $62\mathrm{.}08l\frac{b}{t^3}?$ Recall the pump is rated at $275ft-l\frac{b}{sec}$

In a location where water weighs $62\mathrm{.}08l\frac{b}{f}{t}^3.$ it would take $[$ of work to empty the tank. The pump can pump the tank dry in $$ minutes. It will take the pi

What are the answers to parts a $.$ through c $.$ in a location where water weighs $62\mathrm{.}55l\frac{b}{f}{t}^3?l\frac{b}{f}{t}^3?$ Recall the pump is rated at $275ft-l\frac{b}{sec}.$

In a location where water weighs $62\mathrm{.}55l\frac{b}{f}{t}^3,$ it would take $$ of work to empty the tank. The pump can pump the tank dry in $$ minutes. It will take the pi