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

Answer 1

6 hours

Step-by-step 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.