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.
[tex]\frac{1}{x}+\frac{1}{3x} =\frac{1}{9}\\\frac{3+1}{3x} =\frac{1}{9} \\\frac{4}{3x}=\frac{1}{9}[/tex]
Apply cross multiplication
[tex]x=\frac{9\times 4}{3}\\x=\frac{36}{3} \\x=12hours[/tex]
Theo’s sister to paint the fence in 12 hours.
