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(16946) (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?
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let karen take x hours to do the job alone.
so she does 1/x of the job in 1 hour.
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Betty takes 6 hours working alone
so she does 1/6 of the job in 1hour.
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Both together they do 1/6 + 1/x of the job in 1 hour
= (x+6)/6x of the job in 1 hour.
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both together they take 2/3 *x = 2x/3 hours
or they do 3/2x of the job in 1 hour.
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(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.
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m.ananth@hotmail.ca
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
