SOLUTION: A backyard swimming pool has two fill pipes and a drain pipe. The pool fills in 9 hours with the first fill pipe. Draining the pool with the drain pipe takes 1 hour longer than fil

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A backyard swimming pool has two fill pipes and a drain pipe. The pool fills in 9 hours with the first fill pipe. Draining the pool with the drain pipe takes 1 hour longer than fil      Log On


   

Question 831441: A backyard swimming pool has two fill pipes and a drain pipe. The pool fills in 9 hours with the first fill pipe. Draining the pool with the drain pipe takes 1 hour longer than filling the pool with the second fill pipe. If all three pipes are open at once, the pool can be filled in 8 hours. How many hours would draining the pool take with the two fill pipes closed?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A backyard swimming pool has two fill pipes and a drain pipe.
The pool fills in 9 hours with the first fill pipe.
Draining the pool with the drain pipe takes 1 hour longer than filling the pool with the second fill pipe.
If all three pipes are open at once, the pool can be filled in 8 hours.
How many hours would draining the pool take with the two fill pipes closed?
:
let d = time for the drain to empty the pool, when the other two pipes are closed.
then
(d-1) = time for the 2nd pipe to fill the pool
:
Let the filled pool = 1
8%2F9 + 8%2F%28%28d-1%29%29 - 8%2Fd = 1
multiply equation by 9d(d-1), cancel the denominators, resulting in
8d(d-1) + 9d(8) - 9(d-1)(8) = 9d(d-1)
8d^2 - 8d + 72d - 72d + 72 = 9d^2 - 9d
8d^2 - 8d + 72 = 9d^2 - 9d
combine like terms on the right
0 = 9d^2 - 8d^2 - 9d + 8d - 72
d^2 - d - 72 = 0
Factors to
(d-9(d+8) = 0
The positive solution
d = 9 hrs to drain the pool
:
See if the works
8%2F9 + 8%2F8 - 8%2F9 = 1; looks OK