SOLUTION: A swimming pool is to be filled using two pipes that individually can fill the pool in 8 and 12 hours. The pool drain can empty the pool in 15 hours. How long would it take to fill

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: A swimming pool is to be filled using two pipes that individually can fill the pool in 8 and 12 hours. The pool drain can empty the pool in 15 hours. How long would it take to fill      Log On


   

Question 198741: A swimming pool is to be filled using two pipes that individually can fill the pool in 8 and 12 hours. The pool drain can empty the pool in 15 hours. How long would it take to fill the pool if the two pipes were turned on at the same time, but the drain was accidentally left open?
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
let x="time to fill pool" (in hours)

in x hours, the 8 hour pipe fills x/8 of the pool

in x hours, the 12 hour pipe fills x/12 of the pool

in x hours, the 15 hour drain empties x/15 of the pool

the fractions total to 1, one full pool

x/8 + x/12 - x/15 = 1

multiplying by 120 (LCD) ___ 15x + 10x - 8x = 120

17x = 120 ___ x = 120/17 ___ x = 7.06 (approx)