SOLUTION: I can't figure out the right equation for this problem... I tried setting it to: x/3 + x/9= 1 because similar problems in my homework used the same type of equation but it doesn't

Algebra ->  Rate-of-work-word-problems -> SOLUTION: I can't figure out the right equation for this problem... I tried setting it to: x/3 + x/9= 1 because similar problems in my homework used the same type of equation but it doesn't      Log On


   

Question 33497: I can't figure out the right equation for this problem...
I tried setting it to: x/3 + x/9= 1 because similar problems in my homework used the same type of equation but it doesn't work out correctly...
A pool can be filled by a pipe in 3 hours. It takes three times as long for another pipe to empty the pool. How long will it take to fill the pool with both pipes open.
thank you
Found 2 solutions by stanbon, Earlsdon:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Notice that one pipe is filling and the other is emptying the pool.
Let "x" be the number of hours required to fill the pool.
Filling pipe Data:
time to fill= 3 hr rate= (1/3)job/hr work done= (1/3)x
Emptying pipe Data:
time to empty=9 hr rate= (1/9)job/hr work done = (1/9)x
EQUATION:
fill - emptying = 1 job
Let "x" be the number of hours the job takes.
(1/3)x - (1/9)x = 1
3x - x = 9
2x=9
x=4.5 hours (pool will be full after 4.5 hours)
Cheers,
Stan H.

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
You're on the right track but recognise that while one pipe is filling (positive) the pool the other is emptying (negative) the pool. So if you modify your equation to show that, you'll come out ok.
x%2F3+-+x%2F9+=+1 Simplify.
3x%2F9+-+x%2F9+=+1
2x%2F9+=+1 Multiply both sides by 9.
2x+=+9 Finally, divide both sides by 2.
x+=+4.5
Answer is: 4.5 hours.