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) About Me  (Show Source):
You can put this solution on YOUR website!
Let 1%2Fb = rate that Bob's hose alone fills pool (1 pool/ b hrs)
Let 1%2Fj = rate that Jim's hose alone fills pool (1 pool/ j hrs)
Let 1%2Fx = rate that both hoses fill pool (1 pool/ x hrs)
Then
(1) 1%2Fb+%2B+1%2Fj+=+1%2Fx
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given:
1%2Fx+=+1%2F24 (1 pool)/(24 hrs)
1%2Fb+=+1%2F%28j+-+.4j%29
(2) 1%2Fb=+1%2F%28.6j%29
and, from (1)
(1) 1%2Fb+%2B+1%2Fj+=+1%2F24
These are 2 equations and 2 unknowns, so it's solvable
By substitution:
1%2F%28.6j%29+%2B+1%2Fj+=+1%2F24
Multiply both sides by .6j
1+%2B+.6+=+%28.6j%29%2F24
.6j+=+24+%2B+14.4
j+=+38.4%2F.6
j+=+64
and, from (2),
1%2Fb+=+1%2F%28.6%2A64%29
1%2Fb+=+1%2F38.4
b+=+38.4
Bob's hose alone takes 38.4 hrs
Jim's hose alone takes 64 hrs
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check answer:
(1) 1%2Fb+%2B+1%2Fj+=+1%2F24
1%2F38.4+%2B+1%2F64+=+1%2F24
1%2F384+%2B+1%2F640+=+1%2F240
I'll just convert to decimals:
.002604167+%2B+.0015625+=+.00416667
.004166667+=+.00416667
close enough