Question 863186
The description seems ambiguous regarding the continuous waste removal, but that process is not important to the question.  IF sludge is being added, continuous waste removal is unspecified, and might be assumed not happening.


Fill rate for the empty pool:  {{{1/15+1/21}}}
{{{(7+5)/(3*5*7)}}}
{{{12/105}}}, pools per day, or {{{8&3/4}}} days to fill the sludge pool.