The average sewage flow at a small pumping station is $10000\frac{L}{d},$ while the minimum and maximum flows are $15000\frac{L}{d}$ and $400000\frac{L}{d}.$ Two identical $400000\frac{L}{d}$ pumps are used alternately.

a$)$ Compute the maximum volume, $V,$ of the wet well if the pumps must not be in operation more than two minutes $($pumping time or $t_p)$ per pumping cycle $($during the pumping time of a complete pumping cycle the water level is lowered from its maximum level to its minimum level$).$ For this computation, use the minimal sewage flow.

b$)$ What is the longest time required to fill the wet well? Answers to this questions are a$)$ V$=534\mathrm{.}72$ L

b$)$ maximum filling time $=51\mathrm{.}3$ minutes