Answer: 3 hours
Step-by-step explanation:
Here is the correct question:
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?
Since Betty takes 6 hours to paint a house alone, that means she can paint 1/6 of the house in 1 hour.
Karen can also paint 1/x in 1 hour
Both of them will paint the house in 3/2 hours.
We then add them together which gives:
1/6 + 1/x = 3/2x
The lowest common multiple is 6x
1x/6x + 6/6x = 9/6x
We then leave out the denominators
1x + 6 = 9
x = 9 - 6
x = 3
Karen working alone will paint a house in 3 hours.
