Nextdoor neighbors Bob and Jim use hoses from both houses to

Next-door neighbors Bob and Jim use hoses from both houses to fill Bob\'s swimming pool. They know that it takes 18 hours using both hoses. they also know that bob\'s house, used alone, take 20 percent less time than Jim\'s hose alone. How much time is required to fill the pool by each hose alone?

Solution

Let Jim\'s hose take x hours
it does 1/x of job in 1 hour

Bob\'s hose will take 0.8x hours ( 20 percent less)
it does 1/0.8x of the job in 1 hour

together they take 18 hours
so they do 1/18 of the job in 1 hour

1/x + 1/0.8x = 1/18
1/x + 1.25/x = 1/18
multiply by 18x
18+18*1.25 = x
x= 40.5 hours Jim\'s hose

Bobs hose will tale 0.8*40.5 = 32.4 hours