We are given that Josephine completes a task in 11 hours and she together with her assistant completes the task in 6 hours. To determine the amount of time it would take the assistant alone, we will use the following relationship:
[tex]\frac{1}{t_T}=\frac{1}{t_1}+\frac{1}{t_2}[/tex]
Where:
[tex]\begin{gathered} t_T=\text{ time to complete the task together} \\ t_1=\text{ time to complete the tast by Joseph}ine \\ t_2=\text{ time to complete the tast by her assistant} \end{gathered}[/tex]
If we substitute the known values we get:
[tex]\frac{1}{6}=\frac{1}{11}+\frac{1}{t_2}[/tex]
Now we solve for t2. First we subtract 1/11 from both sides:
[tex]\frac{1}{6}-\frac{1}{11}=\frac{1}{t_2}[/tex]
Solving the operation we get:
[tex]\frac{5}{66}=\frac{1}{t_2}[/tex]
Now we invert both sides:
[tex]\frac{66}{5}=t_2[/tex]
Therefore, it would take the assistant 66/5 or 13.2 hours.
