SOLUTION: Thank you very much to anyone who solves this problem. The pool can be filled in 8 hours and 30 minutes with a red hose. If I run a red and a green hose together, the pool can be

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Thank you very much to anyone who solves this problem. The pool can be filled in 8 hours and 30 minutes with a red hose. If I run a red and a green hose together, the pool can be      Log On


   

Question 371768: Thank you very much to anyone who solves this problem. The pool can be filled in 8 hours and 30 minutes with a red hose. If I run a red and a green hose together, the pool can be filled in 5 hours and 15 minutes. How long would it take to fill up the pool with the green hose only?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The pool can be filled in 8 hours and 30 minutes with a red hose.
If I run a red and a green hose together, the pool can be filled
in 5 hours and 15 minutes.
How long would it take to fill up the pool with the green hose only?
:
Change 8 hrs 30 min to 8.5 hrs
Change 5 hrs 15 min to 5.25 hrs
:
let g = time required by the green hose only
:
Let the completed job = 1 (a full pool)
:
A typical shared work problem
Each hose will do a fraction of the job, the two fractions add up to 1.
:
5.25%2F8.5 + 5.25%2Fg = 1
multiply by 8.5g to clear the denominators, results:
5.25g + 8.5(5.25) = 8.5g
:
5.25g + 44.625 = 8.5g
:
44.625 = 8.5g - 5.25g
:
44.625 = 3.25g
g = 44.625%2F3.25
g = 13.73 hrs which is: 13 + .73(60) = 13 hrs 44 min
:
:
See if that checks out
5.25/8.5 + 5.25/13.73 =
.617 + .382 = .999 ~ 1,
:
How about this? Did it make sense to you?