SOLUTION: 6 children and 2 men complete a certain peice of work in 6 days ,each child takes twice the time teken by a man to fifnish the work ,in how many days will 6 men ll finish the work?

Question 657201: 6 children and 2 men complete a certain peice of work in 6 days ,each child takes twice the time teken by a man to fifnish the work ,in how many days will 6 men ll finish the work?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
THE FIFTH GRADER SOLUTION:
If "each child takes twice the time taken by a man to finish the work", then 2 children do the same work as 1 man, and 6 children would do the work of 3 men.
Then, 6 children and 2 men would do the same work as 3 men and another 2 men, which adds up to 5 men.
The amount of work done was 5 men times 6 days or man-days.
Obviously, 6 men working days will also finish the same man-days job.

WHAT THE TEACHER EXPECTS,
I am not exactly sure, because there are many problem-solving recipe books.
I do not know what recipe your teacher uses, but I will try my best guess.
The amount of work done by a person or a group (or some sort of machine, divided by the time worked is the rate of work.

once we know the rate of work, we can calculate work done over a given period of time, or time required to finish a given amount of work
If one man would take days to finish the job by himself, then a child would take days.
A man's rate of work would be , in jobs per day.
(We could call that the rate of work of a man, , in jobs per day, and we would save ourselves from writing so many denominators).
A child's rate of work would be
The rate of work for a group would be found adding the rates for all the members of the group.
The rate of work for 6 men would be .
The rate of work for 2 men and 6 children would be

The group of 2 men and 6 children completed 1 job in 6 days, so
job
The group of 6 mean would complete the same job in days, so

Multiplying both sides times , which we know is not zero,
--> --> days.
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