SOLUTION: I have tried doing quite a few of these but the example in the book is different, please help me! An inlet pipe on a swimming pool can be used to fill the pool in 15 hours. The

Algebra ->  Rational-functions -> SOLUTION: I have tried doing quite a few of these but the example in the book is different, please help me! An inlet pipe on a swimming pool can be used to fill the pool in 15 hours. The       Log On


   

Question 909520: I have tried doing quite a few of these but the example in the book is different, please help me!
An inlet pipe on a swimming pool can be used to fill the pool in 15 hours. The drain pipe can be used to empty the pool in 24 hours. If the pool is 1/4 filled and then the inlet pipe and drain pipe are opened, how long from that time will it take to fill the pool?
Found 2 solutions by josgarithmetic, richwmiller:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
RT=V rate time volume;
T units of minutes and V units of POOL, the amount of pools.

The filling rate will be 1%2F15-1%2F24 POOLS per MINUTE when both pipes are open. The pool is already %281%2F4%29, so the situation is to fill 3%2F4 pool.

Let t be the time in minutes to fill 3%2F4 pool.

highlight%28%281%2F15-1%2F24%29t=3%2F4%29.
Solve for t.

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
We subtract for the drain pipe.
We are doing 3/4 of the job since the pool is 1/4 filled
x/15-x/24=3/4
x/15-x/24=3/4
24x/360-15x/360=3/4
8x/120-5x/120=3/4
3x=3/4*120
3x=3*30
x=30 hours
check
10/15-10/24=3/4
720/360-450/360=3/4
240/360-150/360=1/4
90/360=1/4
1/4=1/4
ok