<PRE><B>Question 1160431</B>
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It will take the two pumps ? days to empty the pool together.
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It will take the two pumps {{{highlight(1/(1/7+1/11))}}} days to empty the pool together.


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Two different pumps, can empty a pool, ONE pool.
The rates of these pumps in POOL per DAYS:
{{{1/7}}}  and  {{{1/11}}}.


If both pumps are working at the same time, then their combined rate is  {{{1/7+1/11}}}

{{{(11/11)(1/7)+(7/7)(1/11)}}}

{{{11/77+7/77}}}

{{{18/77}}}---------again this rate is POOLs PER DAYS.



Your questions asks for how many DAYS per POOL.  This is the reciprocal , or  {{{77/18}}} DAYS to empty this ONE pool.    You can do the necessary arithmetic.</PRE>