SOLUTION: I need help with this quadratic equation word problem. Working alone, Colleen can paint a house in 2 hours less than James. Working together, they can paint the house in 10 hours.

Question 593458: I need help with this quadratic equation word problem.
Working alone, 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 paint the house by himself?

Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
Let james take x hours to do the job alone.
He does 1/x of the job in 1 hour
Colleen takes x-2 hours
she does 1/(x-2) of the job in 1 hour
Together they take 10 hours
They do 1/10 of the job in 1 hour

LCD = x(x-2)
Multiply the equation by the LCD

10x-20 +10x = x^2-2x
x^2-2x-20x+20=0
x^2-22x+20=0
Find the roots of the equation by quadratic formula

a= 1 , b= -22 , c= 20

b^2-4ac= 484 + -80
b^2-4ac= 404

x1=( 22 + 20.1 )/ 2
x1= 21.05
x2=( 22 -20.1 ) / 2
x2= 0.95
0.95 is not possible
James takes 21 hours to do the job alone

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