SOLUTION: Three brothers decide to paint their house. Kevin could paint the house in 12 hours, and Nick could paint it in 15 hours. When they work together with their brother, Joe, it only t

Question 769245: Three brothers decide to paint their house. Kevin could paint the house in 12 hours, and Nick could paint it in 15 hours. When they work together with their brother, Joe, it only takes five hours to paint the whole house. How long would it take Joe to paint the house if he worked alone?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Three brothers decide to paint their house. Kevin could paint the house in 12 hours, and Nick could paint it in 15 hours. When they work together with their brother, Joe, it only takes five hours to paint the whole house. How long would it take Joe to paint the house if he worked alone?
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Kevin rate: 1/12 job/hr
Nick rate = 1/15 job/hr
together rate = 1/5 job/hr
Joe rate = 1/x job/hr
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Equation:
rate + rate +rate = together rate
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1/12 + 1/15 + 1/x = 1/5
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(15*5x) + (12*5x) + (12*15*5) = (12*15x)
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75x + 60x + 900 = 180x
45x = 900
x = 20 hours (time for Joe to do the job alone)
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Cheers,
Stan H.
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