SOLUTION: After Hurricane Bob, the Duvals needed to remove water from thier flooded basement. They had a sump pump and borrowed a second from a local fire department. The chief explained tha

Question 365335: After Hurricane Bob, the Duvals needed to remove water from thier flooded basement. They had a sump pump and borrowed a second from a local fire department. The chief explained that he expects both pumps working together will empty the basement in 6 hours. The fire dept. sump pump has a higher horsepower and would empty the basement itself in 2 hours less time than the Duval's pump alone. how long would it take each pump to empty the cellar if each were working alone?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The chief explained that he expects both pumps working together will empty the basement in 6 hours. The fire dept. sump pump has a higher horsepower and would empty the basement itself in 2 hours less time than the Duval's pump alone. how long would it take each pump to empty the cellar if each were working alone?
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together rate = 1/6 job/hr
fire dept rate : 1/(x-2) job/hr
Duval pump rate: 1/x job/hr
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Equation:
rate + rate = together rate
1/x + 1/(x-2) = 1/6
6(x-2) + 6x = x(x-2)
6x-12 + 6x = x^2-2x
x^2 -14x + 12 = 0
Positive solution:
x = 13.08 (Duval pump rate)
x-2 = 11.08 hrs. (fire dept rate)
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Cheers,
Stan H.

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