SOLUTION: Working alone, Steve can paint a house in 2 hours less than Gary. Working together, they can paint a house in 10 hours. How long would it take Gary to paint the house by himself?

Question 33180: Working alone, Steve can paint a house in 2 hours less than Gary. Working together, they can paint a house in 10 hours. How long would it take Gary to paint the house by himself?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Steve Data:
time=x-2 hrs/job rate = 1/(x-2) job/hr
Gary Data:
time= x hrs/job rate= 1/x job/hr
Working together Data:
time= 10 hrs/job rate=1/10 job/hr.
EQUATION:
rate + rate = 1/10
1/(x-2) + 1/x = 1/10
10x +10(x-2)= x(x-2)
20x-20 = x^2-2x
x^2-22x+20=0

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=404 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 21.0498756211209, 0.95012437887911. Here's your graph:

From this you see x=21.05 hrs (amount of time Gary requires to do the job alone. It can't be x=0.95 for then Steve's time(x-2) would be negative.
Cheers,
Stan H.
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