# SOLUTION: Colleen can paint a house in 2 hours less than james. Working together they can paint the house in 10 hours. How long would it take james to pain the house by himself?

Algebra ->  Algebra  -> Rate-of-work-word-problems -> SOLUTION: Colleen can paint a house in 2 hours less than james. Working together they can paint the house in 10 hours. How long would it take james to pain the house by himself?      Log On

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 Click here to see ALL problems on Rate-of-work-word-problems Question 308472: Colleen can paint a house in 2 hours less than james. Working together they can paint the house in 10 hours. How long would it take james to pain the house by himself?Answer by mananth(12270)   (Show Source): You can put this solution on YOUR website!Colleen can paint a house in 2 hours less than james. Working together they can paint the house in 10 hours. How long would it take james to pain the house by himself? let james take x hours to paint the house. He will paint 1/x of the house in 1 hour. . . Colleen takes x-2 hours to do the same job she will paint 1/ x-2 of the job in 1 hour .. They both can do the same job in 10 hours they do 1/10 of the job in 1 hour . 1/x + 1/ x-2 = 1/10 add the fractions: LCM = x(x-2) x-2 + x / x(x-2) = 1/10 2x-2 = x(x-2) /10 10(2x-2) = x(x-2) 20x-40= x^2-2x x^2-22x+40=0 x^2 -20x-2x+40=0 x(x-20)-2(x-20)=0 (x-20)(x-2)=0 x= 20 OR 2 hours So James can paint the house alone in 20 hours