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?
:
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
{{{8/9}}} + {{{8/((d-1))}}} - {{{8/d}}} = 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
{{{8/9}}} + {{{8/8}}} - {{{8/9}}} = 1; looks OK