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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)
x= 20 OR 2 hours
So James can paint the house alone in 20 hours