Answer: Annette will take 6 hours to do the entire job alone.
Step-by-step explanation:
Given: Time taken by Kelly to do [tex]\dfrac{1}{5}[/tex] of job = 2 hours
i.e. Time for complete job done alone by Kelly =[tex]5\times2=10\ hours[/tex]
Rest of work = [tex]1-\dfrac{1}{5}=\dfrac{4}{5}[/tex] of the job
[tex]\dfrac{4}{5}[/tex] of the complete job done by both Kelly and Annette in 3 hours
Time would be taken by then to do entire job together = [tex]3\times\dfrac{5}{4}=3.75\ hours[/tex]
Let t be the time taken by Annette to do job alone.
Then, as per situation
[tex]\dfrac{1}{3.75}=\dfrac{1}{10}+\dfrac{1}{t}\\\\\Rightarrow\ \dfrac{1}{t}=\dfrac{1}{3.75}-\dfrac{1}{10}\\\\\Rightarrow\ \dfrac{1}{t}=\dfrac{4}{15}-\dfrac{1}{10}\\\\\Rightarrow\ \dfrac{1}{t}=\dfrac{1}{6}\\\\\Rightarrow\ t=6[/tex]
hence, Annette will take 6 hours to do the entire job alone.
