Question 746611
Add the rates of filling of the 2 filling pipes and
subtract the rate of draining of the emptying pipe
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1st pipe's rate:  ( 1 pool filled ) / ( 3 hrs )
2nd pipe's rate: ( 1 pool filled ) / ( 6 hrs )
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3rd pipe's rate of emptying: ( 1 pool emptied ) / ( 4 hrs )
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Let {{{ t }}} = the time in hrs to fill the pool with all 3 pipes open
{{{ 1/3 + 1/6 -1/4 = 1/t }}}
Multiply both sides by {{{ 24t }}}
{{{ 8t + 4t - 6t = 24 }}}
{{{ 6t = 24 }}}
{{{ t = 4 }}}
It will take 4 hrs to fill the pool with all 3 pipes open
check:
{{{ 1/3 + 1/6 -1/4 = 1/t }}}
{{{ 1/3 + 1/6 -1/4 = 1/4 }}}
Add {{{ 1/4 }}} to both sides
{{{ 1/3 + 1/6 = 1/2 }}}
{{{ 2/6 + 1/6 = 1/2 }}}
{{{ 3/6 = 1/2 }}}
{{{ 1/2 = 1/2 }}}
OK