The rectangular tank shown here, with its top at ground level, is used to catch runoff water. Assume that the water weighs $62\mathrm{.}4l\frac{b}{f}{t}^3.$

a$.$ How much work does it take to empty the tank by pumping the water back to ground level once the tank is full?

b$.$ If the water is pumped to ground level with a $(\frac{5}{11})-$horsepower $($hp$)$ motor $($work output $250ft-l\frac{b}{sec}),$ how long will it take to empty the tank $($to the nearest minute$)?$

c$.$ Show that the pump in part $($b$)$ will lower the water level $20$ ft $($halfway$)$ during the first $100$ minutes of pumping.

d$.$ What are the answers to parts $($a$)$ and $($b$)$ in a location where water weighs $62\mathrm{.}11l\frac{b}{f}{t}^3?62\mathrm{.}51l\frac{b}{f}{t}^3?$