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 12 h to paint a house alone. How long does it take Karen to paint a house working alone

6 hours

Explanation:

Let k = time it takes Karen to paint the house alone

then according to the question,

(2/3) (k) (1/k + 1/12) = 1

⇒ (2k/3) (1/k + 1/12) = 1

⇒ (2k) (1/k + 1/12) = 3

⇒ (2 + k/6) = 3

Multiplying both sides by 6:

12 + k = 18

k = 6 hours

therefore Karen takes 6 hours to complete the Task.