SOLUTION: Next-door neighbors Bob and Jim use hoses from both houses to fill Bob's swimming pool. They know it takes 24 h using both hoses. They also know that Bob's hose, used alone, takes
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Question 397853: Next-door neighbors Bob and Jim use hoses from both houses to fill Bob's swimming pool. They know it takes 24 h using both hoses. They also know that Bob's hose, used alone, takes 40% less time than Jim's hose alone. How much time is required to fill the pool by each hose alone?
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = rate that Bob's hose alone fills pool (1 pool/ b hrs)
Let = rate that Jim's hose alone fills pool (1 pool/ j hrs)
Let = rate that both hoses fill pool (1 pool/ x hrs)
Then
(1)
-----------------
given:
(1 pool)/(24 hrs)
(2)
and, from (1)
(1)
These are 2 equations and 2 unknowns, so it's solvable
By substitution:
Multiply both sides by
and, from (2),
Bob's hose alone takes 38.4 hrs
Jim's hose alone takes 64 hrs
-------------------------
check answer:
(1)
I'll just convert to decimals:
close enough
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