Question 795464
Add the positive rate of filling to the
negative rate of draining to get the
rate when you are both filling and 
draining
-------------
Rate of filling:
( 1 sink full ) / ( 5 min )
Rate of draining:
( 1 sink drained ) / ( 10 min )
-------------------------
Let {{{ t }}} = time to fill sink while
both filling and draining
---------------------
{{{ 1/5 - 1/10 = 1/t }}}
( note that if  the right side is positive, 
the result is filling, not draining )
----------------------
Multiply both sides by {{{ 10t }}}
{{{ 2t - t = 10 }}}
{{{ t = 10 }}}
It will it take 10 min to fill the sink if 
you forget to put in the stopper