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

Answer:

12 hours

Step-by-step 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.

$\frac{1}{x}+\frac{1}{3x} =\frac{1}{9}\\\frac{3+1}{3x} =\frac{1}{9} \\\frac{4}{3x}=\frac{1}{9}$

Apply cross multiplication

$x=\frac{9\times 4}{3}\\x=\frac{36}{3} \\x=12hours$

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