SOLUTION: Next door neighbors Angelina and Brad use hoses from both houses to fill Brad's swimming pool. They know it takes 18 hours using both hoses. They also know that Brad's hose, used a

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Next door neighbors Angelina and Brad use hoses from both houses to fill Brad's swimming pool. They know it takes 18 hours using both hoses. They also know that Brad's hose, used a      Log On


   

Question 589241: Next door neighbors Angelina and Brad use hoses from both houses to fill Brad's swimming pool. They know it takes 18 hours using both hoses. They also know that Brad's hose, used alone, takes 20% less time than Angelina's hose alone. Calculate how much tim eis required to fill the pool by each hose alone.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Next door neighbors Angelina and Brad use hoses from both houses to fill Brad's swimming pool.
They know it takes 18 hours using both hoses.
They also know that Brad's hose, used alone, takes 20% less time than Angelina's hose alone.
Calculate how much time is required to fill the pool by each hose alone.
:
let t = time required by A's hose alone
B takes 20% less time, therefore
.8t = time required by B's hose alone
:
Let the completed job = 1; (a full pool)
:
18%2Ft + 18%2F%28.8t%29 = 1
Multiply by 8t to clear the denominators
8t*18%2Ft + 8t*18%2F%28.8t%29 = 8t
Cancel the denominators
8(18) + 10(18) = 8t
144 + 180 = 8t
324 = 8t
t = 324/8
t = 40.5 hrs A's hose alone
then
.8*40.5 = 32.4 hrs, B's hose
:
:
See if the checks out
18%2F40.5 + 18%2F32.4 =
.444 + .555 = .999 ~ 1, confirms our solutions