# SOLUTION: Betty and karen have been hired to paint the houses in a new development. Working together the women can paint a house in two thirds the time that it takes karen working alone. Bet

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 Question 199036This question is from textbook algebra and trigonometry : Betty and karen have been hired to paint the houses in a new development. Working together the women can paint a house in two thirds the time that it takes karen working alone. Betty takes 6 hours to paint a house alone. How long does it take karen to paint a house working alone?This question is from textbook algebra and trigonometry Answer by nerdybill(6962)   (Show Source): You can put this solution on YOUR website! Betty and karen have been hired to paint the houses in a new development. Working together the women can paint a house in two thirds the time that it takes karen working alone. Betty takes 6 hours to paint a house alone. How long does it take karen to paint a house working alone? . Let k = time it takes Karen to paint the house alone then (2/3)(k)(1/k + 1/6) = 1 (2k/3)(1/k + 1/6) = 1 (2k)(1/k + 1/6) = 3 (2 + k/3) = 3 Multiplying both sides by 3: 6 + k = 9 k = 3 hours