SOLUTION: I am supposed to set up a quadratic equation for this word problem, but I don't see how to do that. The problem is: Working alone, Colleen can paint a house in 2 hours less tha

Algebra ->  Algebra  -> Quadratic Equations and Parabolas -> SOLUTION: I am supposed to set up a quadratic equation for this word problem, but I don't see how to do that. The problem is: Working alone, Colleen can paint a house in 2 hours less tha      Log On

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Question 84190This question is from textbook Algebra Structure and Method
: I am supposed to set up a quadratic equation for this word problem, but I don't see how to do that. The problem is:
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 pain the house by himself.This question is from textbook Algebra Structure and Method

Answer by ankor@dixie-net.com(15660) About Me  (Show Source):
You can put this solution on YOUR website!
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 pain the house by himself.
:
Let x = time required by James by himself
Let the completed job = 1
:
Fraction done by James + Fraction done by Colleen = 1
10%2F%28%28x-2%29%29 + 10%2Fx = 1
:
Mult equation by x(x-2) to get rid of the denominators:
10x + 10(x-2) = x(x-2)
;
10x + 10x - 20 = x^2 - 2x
:
20x = x^2 - 2x + 20
:
x^2 - 2x - 20x + 20 = 0;
:
x^2 - 22x + 20 = 0; the quadratic equation, you sought after.
:
Use the quadratic formula to solve, only one solution will make sense.