SOLUTION: It takes a smaller hose twice as long to fill a certain swimming pool as it does a larger holes. It takes both hoses working together 25 minutes to fill the pool. How long will

Algebra ->  Human-and-algebraic-language -> SOLUTION: It takes a smaller hose twice as long to fill a certain swimming pool as it does a larger holes. It takes both hoses working together 25 minutes to fill the pool. How long will       Log On


   

Question 1140860: It takes a smaller hose twice as long to fill a certain swimming pool as it does a larger holes. It takes both hoses working together 25 minutes to fill the pool. How long will it take the larger hose to fill the pool by it self? Do not do any rounding.
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
small hose rate 1%2F%282x%29
large hose rate 1%2Fx
combined hose rate 1%2F25

1%2F%282x%29%2B1%2Fx=1%2F25
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multiply both sides by 50x.
25%2B50=2x
75=2x
highlight%28x=75%2F2%29---------LARGE hose time by itself
75--------time for SMALL hose

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CHECK:
1%2F%282%2A%2875%2F2%29%29%2B1%2F%2875%2F2%29=1%2F25?
1%2F75%2B2%2F75
3%2F75
3%2F%283%2A25%29
1%2F25--------same as right-side
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2x=2%2A%2875%2F2%29=75 works.

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


When working together, the two hoses fill the pool in 25 minutes. Since the smaller hose takes twice as long as the smaller to fill the pool, the larger hose does twice as much work as the smaller.

That means that in 25 minutes working together the larger hose does 2/3 of the job of filling the pool.

And that means the larger hose will take 3/2 times 25 minutes to fill the pool alone.

ANSWER: 25*(3/2) = 75/2 = 37.5 minutes