We can do the following steps to solve the exercise:
Step 1: We convert the mixed number to an improper fraction.
[tex]1\frac{1}{9}=\frac{1\cdot9+1}{9}=\frac{9+1}{9}=\frac{10}{9}[/tex]Step 2: We divide the total number of acres of trees cut by the total number of weeks.
[tex]\begin{gathered} \text{ Number of acres cut per week }=\frac{\frac{10}{9}}{3} \\ \text{ Number of acres cut per week }=\frac{\frac{10}{9}}{\frac{3}{1}} \\ \text{ Number of acres cut per week }=\frac{10\cdot1}{9\cdot3} \\ \text{ Number of acres cut per week }=\frac{10}{27} \end{gathered}[/tex]Therefore, they did cut 10/27 acres per week.