SOLUTION: Betty and Karen have been hired to paint the house in the new development. Working together the women can paint a house in two-thirds the time it takes Karen working alone. Betty

Question 1084879: Betty and Karen have been hired to paint the house in the new development. Working together the women can paint a house in two-thirds the time it takes Karen working alone. Betty takes 12 hours to paint a house alone. How long does it take Karen to paint a house working alone?
Answer by jorel1380(3719) (Show Source): You can put this solution on YOUR website!
Let b be Betty, and k be Karen, and n be the time it takes Karen to complete the job. Then:
1/k=1/n
So:
1/b+1/k=1/((2n)/3)
1/12+1/n=3/2n
n+12=18
n=6
n=6, so k=6, then it takes Karen 6 hours to paint the house alone. Working together, they finish the house in 4 hours. ☺☺☺☺

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