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?

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(16946) (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

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