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Question 832254: Hi! My question is:
Next-door neighbors Bob and Jim use hoses from both houses to fill Bob's swimming pool. They know that it takes 18h using both hoses. They also know that Bob's hose, used alone, takes 20% less time than Jim's hose alone. How much time is required to fill the pool by each hose alone?
The book gives you an example of how to solve for the time it would take to use both, but there is no example for solving for each in an equation. Do I need to set up two separate equations?
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! let bhose be the time for Bob's hose and jhose be the time for Jim's hose, then
the contributions per hour is described by the following equation
1/bhose + 1/jhose = 1/18
also we know
bhose = jhose - .20jhose
note that 1/bhose represents how much work bhose does per hour and 1/jhose represents how much work jhose does per hour
knowing this let's substitute for bhose in our first equation
1/(jhose - .20jhose) + 1/jhose = 1/18
1/(.80jhose) + 1/jhose = 1/18
multiply both sides of = by jhose
1/.80 + 1 = jhose/18
2.25 = jhose /18
jhose = 2.25 * 18 = 40.5 hours
bhose = 40.5 - (0.20*(40.5)) = 32.4 hours
check the answer
1/32.4 + 1/40.5 = 1/18
0.03086419753086419753 + 0.02469135802469135802 = 0.05555555555555555556
0.05555555555555555556 = 0.05555555555555555556
answer checks
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