SOLUTION: Carlos can paint a room in three hours less time than Reggie. If both men work together, they can complete plainting the entire room in two hours. How long would it take for Carlos

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Question 39415: Carlos can paint a room in three hours less time than Reggie. If both men work together, they can complete plainting the entire room in two hours. How long would it take for Carlos to do the job alone?
This is my work:
2/r-3 + 2/r = 1
Clear fractions be multiplying be (r-3) and (r)
2r + 2r - 6 = r^2 - 3r
subtract r^2 - 3r on each side
-r^2 + r - 6 = 0
Then there is no solution!
Answer by fractalier(2101) (Show Source):
You can put this solution on YOUR website!
Let me show you where you went wrong...you're okay to this point
2/r-3 + 2/r = 1
2r + 2r - 6 = r^2 - 3r
but when you combine terms, you should get
4r - 6 = r^2 - 3r
r^2 - 7r + 6 = 0
(r - 1)(r - 6) = 0
r = 1 or r = 6
but r cannot be 1, so
r = 6
which checks when you plug it in...