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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
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.