Question

in 2 h, kelly laid new floor tile over 1/5 of the room. when she was joined by annette, the rest of the work was completed in 3h. how long would it have taken annette to do the entire job alone

Answer 1

Answer: Annette will take 6 hours to do the entire job alone.

Step-by-step explanation:

Given: Time taken by Kelly to do $\dfrac{1}{5}$ of job = 2 hours

i.e. Time for complete job done alone by Kelly =$5\times2=10\ hours$

Rest of work = $1-\dfrac{1}{5}=\dfrac{4}{5}$ of the job

$\dfrac{4}{5}$  of the complete job done by both Kelly and Annette in 3 hours

Time would be taken by then to do entire job together = $3\times\dfrac{5}{4}=3.75\ hours$

Let t be the time taken by Annette to do job alone.

Then, as per situation

$\dfrac{1}{3.75}=\dfrac{1}{10}+\dfrac{1}{t}\\\\\Rightarrow\ \dfrac{1}{t}=\dfrac{1}{3.75}-\dfrac{1}{10}\\\\\Rightarrow\ \dfrac{1}{t}=\dfrac{4}{15}-\dfrac{1}{10}\\\\\Rightarrow\ \dfrac{1}{t}=\dfrac{1}{6}\\\\\Rightarrow\ t=6$

hence, Annette will take 6 hours to do the entire job alone.