Kim alone = 11 hours
Bethany alone = 6 hours
Let time for Kim and Bethany = t
[tex]\begin{gathered} \frac{1}{11}\text{ + }\frac{1}{6}\text{ = }\frac{1}{t} \\ \frac{6\text{ + 11}}{66}\text{ = }\frac{1}{t} \\ \frac{17}{66}\text{ = }\frac{1}{t} \\ \text{Cross multiply} \\ 17t\text{ = 66} \\ t\text{ = }\frac{66}{17} \\ t\text{ = 3}\frac{15}{17}\text{ hours} \end{gathered}[/tex]