SOLUTION: it takes 90 minutes to remove an amount of water from the basement when two pumps of different sizes are operating. It takes 2 hours to remove the same amount of water when only th

Question 504023: it takes 90 minutes to remove an amount of water from the basement when two pumps of different sizes are operating. It takes 2 hours to remove the same amount of water when only the larger pump is running. How long would it take to remove the same amount of water if only the smaller pump were running?
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
L = amount of water removed by the larger pump per minute
S = amount of water removed by the smaller pump per minute
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working together, they can do 1 whole job in 90 minutes
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90*(L+S) = 1
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working alone, the larger pump can do the job in 120 minutes (2 hr)
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120L = 1
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L = 1/120 of the job per minute
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substitute to find S
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90*(L+S) = 1
90*(1/120 + S ) = 1
1/120 + S = 1/90
S = 1/90 - 1/120
S = 4/360 - 3/360
S = 1/360
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So the smaller pump can do the job at a rate of 1/360 per minute.
360 minutes = 6 hr.
That means it would it it 6 hours working alone.
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Always check your work.
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90(1/120 + 1/360) = ?
90/120 + 90/360 = 3/4 + 1/4 = 1
Correct.
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Re-read the question to make sure you answer it.
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Answer: The smaller pump would take 6 hrs to do the job working alone.
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Done.

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