SOLUTION: I've got a word problem that has me stumped. Here it is: Working together, Kent and Monica can paint the interior of a 2000 square-foot home in 10hours. If Kent paint the hous

Question 79403: I've got a word problem that has me stumped. Here it is:
Working together, Kent and Monica can paint the interior of a 2000 square-foot home in 10hours. If Kent paint the house by himself, it will take 2 hours longer than if Monica paints the home by herself. How long will it take each person to paint the house working alone?
Thanks so much!!
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
:
Working together, Kent and Monica can paint the interior of a 2000 square-foot home in 10hours. If Kent paints the house by himself, it will take 2 hours longer than if Monica paints the home by herself. How long will it take each person to paint the house working alone?
:
Let t = time for M to do the job by herself:
:
It says:"If Kent paint the house by himself, it will take 2 hours longer than if Monica paints the home by herself." therefore:
:
(t+2) = time for K to do the job
:
Let the completed job = 1; (we don't care how big the house is)
:
A simple equation:
+ = 1
:
Multiply equation by t(t+2) and we have:
10(t+2) + 10t = t(t+2)
:
10t + 20 + 10t = t^2 + 2t
:
20t + 20 = t^2 + 2t
:
Arrange as a quadratic equation:
t^2 + 2t - 20t - 20 = 0
:
t^2 - 18t - 20 = 0
:
you will have to use the quadratic formula to find t: a=1; b=-18; c=-20
I got t = -1.05 and t = +19.05, the obvious solution
:
M's time = 19.05 hrs
K's time = 21.05 hrs
:
:
Check our solutions on a calc:
10/19.05 + 10/21.05 = 1.0
:
Could this used as "stump remover" do you think?

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