Question 696749
It doesn't matter that there are 3 pipes. It only matters
that all 3 are open, and, by themselves, they fill
the pool in 8 hrs.
------------------
Add the rate of filling and subtract the rate of draining
to get the rate of filling
----------------------
( 1 pool filled ) / ( 8 hrs ) - ( 1 pool drained ) / ( 12 hrs ) = ( 1/4 pool filled ) ( t hrs )
{{{ 1/8 - 1/12 = (1/4) / t }}}
Bring the {{{ 4 }}} down to the denominator
{{{ 1/8 - 1/12 = 1 /(4t) }}}
Multiply both sides by {{{ 24t }}}
{{{ 3t - 2t = 6 }}}
{{{ t = 6 }}}
1/4 of the pool will be filled in 6 hrs