SOLUTION: Two pipes can be used to fill a pool. Working​ together, the two pipes can fill the pool in 8 hours. The larger pipe can fill the pool in 4 hours less time than the smaller

Algebra ->  Finance -> SOLUTION: Two pipes can be used to fill a pool. Working​ together, the two pipes can fill the pool in 8 hours. The larger pipe can fill the pool in 4 hours less time than the smaller      Log On


   

Question 1113289:
Two pipes can be used to fill a pool. Working​ together, the two pipes can fill the pool in 8 hours. The larger pipe can fill the pool in 4 hours less time than the smaller pipe can alone. Find the time to the nearest tenth of an hour it takes for the smaller pipe working alone to fill the pool.
Found 2 solutions by josgarithmetic, mananth:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
1%2Fx%2B1%2F%28x-4%29=1%2F8
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8%28x-4%29%2B8x=x%28x-4%29
8x-32%2B8x=x%5E2-4x
x%5E2-4x-16x%2B32=0
x%5E2-20x%2B32=0

x=%2820%2B-+sqrt%28400-4%2A32%29%29%2F2
x=%2820%2B-+sqrt%28272%29%29%2F2
x=%2820%2B-+sqrt%2816%2A17%29%29%2F2
x=10%2B-+2%2Asqrt%2817%29
Must use the greater value.
x=10%2B2%2Asqrt%2817%29=18.2462--------time in hours for smaller pipe;
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18.2 hours (nearest tenth of hour)

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!

Filling the pool is 1 job
Pipe A + pipe B takes 8 hours
So they will do 1 / 8 of the job in 1 hour
Pipe A alone takes x hours
It does 1 / x of the job in 1 hour
Pipe B does the job in x -4 hours
Pipe B does 1/(x -4 ) of the job in 1 hour

1/x + 1/(x -4 )= 1 / 8
Simplify
(x -4 +x/((x)(x -4 )= 1 / 8

8 (2x-4)= x^2 -4 x
16 x -32 = x^2 -4 x

x^2- -20 x+ 32 = 0
solve the quadratic equation by formula method
x=18.2
x-4 =14.2
One pipe 18.2 hours to fillalone
Pipe B 14.2 hours to fill alone