SOLUTION: Pipe A fills a swimming pool in 4 hours.Pipe B empties the pool in 6 hours.if pipe A was opened at 8:00am and pipe 9:00am,at what time will the pool be full?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Pipe A fills a swimming pool in 4 hours.Pipe B empties the pool in 6 hours.if pipe A was opened at 8:00am and pipe 9:00am,at what time will the pool be full?      Log On


   

Question 617128: Pipe A fills a swimming pool in 4 hours.Pipe B empties the pool in 6 hours.if pipe A was opened at 8:00am and pipe 9:00am,at what time will the pool be full?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Pipe A fills a swimming pool in 4 hours.
Pipe B empties the pool in 6 hours.
if pipe A was opened at 8:00am and pipe 9:00am,at what time will the pool be full?
:
Let t = the filling time of pipe A
then
(t-1) = the draining time of pipe B
:
Let the completed job = 1 (a full pool)
:
t%2F4 - %28%28t-1%29%29%2F6 = 1
multiply by 12, clear the denominators
12*t%2F4 - 12*%28%28t-1%29%29%2F6 = 12
Cancel the denominators
3t - 2(t - 1) = 12
3t - 2t + 2 = 12
t = 12 - 2
t = 10 hrs; then full pool at: 8:00 Am + 10:00 = 6:00 Pm