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

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 Question 357292: Betty and Karen have been hired to paint the house in a new development. Working together the women can paint a house in two-thirds the lime that it takes Karen working alone. Betty takes 6h to paint a house alone. How long does it take Karen to paint a house working alone?Found 2 solutions by mananth, ewatrrr:Answer by mananth(12270)   (Show Source): You can put this solution on YOUR website!Working together the women can paint a house in two-thirds the lime that it takes Karen working alone. Betty takes 6h to paint a house alone. How long does it take Karen to paint a house working alone? ... let karen take x hours to do the job alone. so she does 1/x of the job in 1 hour. .. Betty takes 6 hours working alone so she does 1/6 of the job in 1hour. ... Both together they do 1/6 + 1/x of the job in 1 hour = (x+6)/6x of the job in 1 hour. ... both together they take 2/3 *x = 2x/3 hours or they do 3/2x of the job in 1 hour. ... (x+6)/6x = 3/2x 2x(x+6)=3x 2x^2+12x=18x 2x^2= 6x divide by 2x x= 3 Karen takes 3 hours to do the job alone. .... m.ananth@hotmail.ca Answer by ewatrrr(10682)   (Show Source): You can put this solution on YOUR website!``` Hi, *Note: takes 2/3 of 6hrs or 4hrs to paint the house together. Let x represenst the time it takes for Karen to paint the house alone Multiplying thru with 24x 4x + 24 = 6x 24 = 2x 12 = x Takes Karen 12 hrs to paint the house alone ```