Question 116939
This is a form of work problem- like when you know how long
it takes for person a to do a job and person b to do a job,
how long does it take when they work together?
For this problem, 
(pipe A's rate of filling pool)+(pipe B's rate of filling pool)
= (rate of A and B together filling pool)
in other words,
(1 pool/6 hrs) + (1 pool/12 hrs) = (1 pool/x hrs)
{{{(1/6) + (1/12) = 1/x}}}
multiply both sides by {{{12x}}}
{{{2x + x = 12}}}
{{{3x = 12}}}
{{{x = 4}}}hrs answer
It takes 4 hrs to fill the pool when both pipes are left open
check answer
{{{(1/6) + (1/12) = 1/x}}}
{{{(1/6) + (1/12) = 1/4}}}
{{{(2/12) + (1/12) = 3/12}}}
{{{3/12 = 3/12}}}
OK