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AlekseyPX
3 years ago
13

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
Mathematics
1 answer:
jeyben [28]3 years ago
7 0

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.

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