Answer & 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.