Solution:
Given:
Courtney can power wash the entire patio in 7 hours while
it takes Joe just 5 hours to power wash the patio
Based on the given information,
Courtney work rate = 1/7
Joe work rate = 1/5
let x represent the number of hours it take Courtney and Joe to power wash the patio together
Thus,
[tex]\begin{gathered} \frac{1}{x}=\frac{1}{7}+\frac{1}{5} \\ \\ \frac{1}{x}=\frac{5+7}{35} \\ \\ \frac{1}{x}=\frac{12}{35} \\ \\ x\text{ =}\frac{35}{12}\text{ hours} \\ \\ x=2\frac{11}{12}\text{ hours} \\ \\ The\text{ answer is 2}\frac{11}{12}hours \end{gathered}[/tex]