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A mother can do a certain job in x hours. Her daughter takes twice as long to do the job. Working together, they can do the job in 6 hours. How many hours does the mother take to do the job ?

Correct Answer: 9

Explanation:

The mother completes the job in x hours.
So, the daughter will take 2x hours to complete the same job.


 


In an hour, the mother will complete 1/x of the total job.
In an hour, the daughter will complete 1/2x of the total job.


 


So, if the mother and daughter work together, in an hour they will complete 1/x + 1/2x of the job.
i.e., in an hour they will complete 3/2x of the job.


 


The question states that they complete the entire task in 6 hours if they work together.
i.e., they complete 1/6 th of the task in an hour.


 


Equating the two information, we get 3/2x = 1/6
By solving for x, we get 2x = 18 or x = 9.


 


The mother takes 9 hours to complete the job.


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