Question 139247
If it takes a small inlet pipe 5 hours to fill a pool, a large pipe 2 hours to fill a pool, and a standard outlet pipe 6 hours to empty a pool how long will it take to fill an empty pool if all three pipes are in operation?
:
Let t = time (in hrs) required to empty the pool
:
Let the full pool = 1
:
Filling (+) and emptying (-)
:
{{{t/5}}} + {{{t/2}}} - {{{t/6}}} = 1
:
Get rid of the denominators, multiply by 30:
6t + 15t - 5t = 30
:
16t = 30
t = {{{30/16}}}
t = 1.875 hrs
:
:
Confirm solution:
{{{1.875/5}}} + {{{1.875/2}}} - {{{1.875/6}}} = 
.375 + .9375 - .3125 = 1