SOLUTION: If three pipes are all opened, they can fill an empty swimming pool in 3 hours. The largest pipe alone takes 1/3 the time that the smallest pipe takes and half the time the other p

Algebra ->  Rate-of-work-word-problems -> SOLUTION: If three pipes are all opened, they can fill an empty swimming pool in 3 hours. The largest pipe alone takes 1/3 the time that the smallest pipe takes and half the time the other p      Log On


   

Question 240503: If three pipes are all opened, they can fill an empty swimming pool in 3 hours. The largest pipe alone takes 1/3 the time that the smallest pipe takes and half the time the other pipe takes. How long would it take each pipe to fill the pool by itself?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
If three pipes are all opened, they can fill an empty swimming pool in 3 hours.
The largest pipe alone takes 1/3 the time that the smallest pipe takes and half the time the other pipe takes.
How long would it take each pipe to fill the pool by itself?
:
To avoid those annoying fractions, do it like this
:
Let t = time required by the largest pipe alone
then
3t = time of the smallest
and
2t = time of the other pipe
:
Let the completed job = 1 (a full pool)
:
3%2Ft + 3%2F%283t%29 + 3%2F%282t%29 = 1
multiply by 6t, results
6(3) + 2(3) + 3(3) = 6t
:
18 + 6 + 9 = 6t
:
33 = 6t
t = 33%2F6
t - 5.5 hrs time of the largest pipe alone
then
3(5.5) = 16.5 hrs time of the smallest pipe
and
2(5.5) = 11 hrs time of the other pipe
:
:
Check solution in the original equation, using a calc:
3%2F5.5 + 3%2F%2816.5%29 + 3%2F%2811%29 =
.545 + .182 + .273 = .9997 ~ 1