Question 690250
One pipe has a positive rate ( filling )
The other pipe has a negative rate ( emptying )
The 1st pipe's rate is ( 1 pool filled ) / ( 9 hrs )
The 2nd pipe's rate is ( 1 pool emptied ) / ( 12 hrs )
Let {{{t}}} = the time in hrs to fill the pool with both pipes open
Add their rates to get their rate working against each other
{{{ 1/9 - 1/12 = 1/t }}} 
Multiply both sides by {{{ 36 }}}
{{{ 36/9 - 36/12 = 36/t }}} 
{{{ 4 - 3 = 36/t }}}
{{{ 36/t = 1 }}}
{{{ t = 36 }}}
With both pipes open, the pool is filled in 36 hrs