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

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(7384) (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

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