Pumping Water 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 $(5/11)-$horsepower motor $($work output $250ft*l\frac{b}{sec}),$ how long will it take to empty the full tank $($to the nearest minute$)?$

$($c$)$ Show that the pump in part $($b$)$ will lower the water level $10$ ft $($halfway$)$ during the first $25$ min of pumping.

$($d$)$ The Weight of Water Because of differences in the strength of Earth's gravitational field, the weight of a cubic foot of water at sea level can vary from as litule as $62\mathrm{.}26$ lb at the equator to as much as $62\mathrm{.}59$ lb near the poles, a variation of about $0\mathrm{.}5\%.$ A cubic foot of water that weighs $62\mathrm{.}4$ lb in Melbourne or New York City will weigh $62\mathrm{.}5$ lb in Juneau or Stockholm. What are the answers to parts $($a$)$ and $($b$)$ in a location where water weighs $62\mathrm{.}26l\frac{b}{t}{t}^3?62\mathrm{.}5l\frac{b}{f}{t}^3?$