Question

Theo can paint a fence three times as fast as his sister can. Working together, they can paint a fence in 9 hours. How many hours would it take Theo’s sister to paint the fence by herself?

Answer 1

12 hours

Explanation:

Let Theo's siste can paint a fence in x times

Given.

Theo can paint a fence three times as fast as his sister can. Working together, they can paint a fence in 9 hours.

`(1)/(x)+(1)/(3x) =(1)/(9)\\(3+1)/(3x) =(1)/(9) \\(4)/(3x)=(1)/(9)`

Apply cross multiplication

`x=(9* 4)/(3)\\x=(36)/(3) \\x=12hours`

Theo’s sister to paint the fence in 12 hours.