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The rectangular tank shown here, with its top at ground level, is used to catch runoff water. Assume that the water weighs $62.5 \mathrm{lb} / \mathrm{ft}^{3}$.$\newline$a. How much work does it take to empty the tank by pumping the water back to ground level once the tank is full?$\newline$b. If the water is pumped to ground level with a ($10$/$11$)-horsepower (hp) motor (work output $500 \mathrm{ft}-\mathrm{lb} / \mathrm{sec}$ ), how long will it take to empty the tank (to the nearest minute)?$\newline$c. Show that the pump in part (b) will lower the water level $10 \mathrm{ft}$ (halfway) during the first $18$ minutes of pumping.$\newline$d. What are the answers to parts (a) and (b) in a location where water weighs$\newline$$62.31 \mathrm{lb} / \mathrm{ft}^{3} ? 62.61 \mathrm{lb} / \mathrm{ft}^{3} ?$$\newline$a. Set up an integral to find the work done.$\newline$$\mathrm{W}=$ $\square$$\newline$How much work does it take to empty the tank?$\newline$$\square$$\newline$b. How long will it take to empty the tank?$\newline$$\square$ minutes (Round to the nearest minute as needed.)$\newline$c. How much work does it take to lower the water level halfway?$\newline$$\square$