SOLUTION: Together, Ray and Debra can paint the house in 12 hours. Working alone, it would take Debra 7 hours more than it would take Ray. How long would it take her to paint the house herse

Question 430046: Together, Ray and Debra can paint the house in 12 hours. Working alone, it would take Debra 7 hours more than it would take Ray. How long would it take her to paint the house herself?
Answer by jorel1380(3719) (Show Source): You can put this solution on YOUR website!
If Ray and Debra can paint a house in 12 hours, then
R+D=12. Therefore; 1/R+1/D=1/12. Since Debra takes 7 more hours than Ray, we have:
1/R+1/(R+7)=1/12

Using the least common factor, we multiply both sides of the equation by (12)(R)(R+7), giving us:
12(R+7)+12R=R^2+7R
12R+84+12R=R^2+7R
24R+84=R^2+7R
0=R^2-17R-84
0=(R-21)(R+4)
R=21, -4
Ignoring the negative result, we get Ray can paint a house alone in 21 hours, so Debra takes 28 hours alone.

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