Question 430046
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.