SOLUTION: Three men can individually do a job in 5, 6 and 7 hours respectively. What is the greatest fractional part of the job that can be done in 2 hours by any two of the men working toge

Question 580007: Three men can individually do a job in 5, 6 and 7 hours respectively. What is the greatest fractional part of the job that can be done in 2 hours by any two of the men working together?
Answer by Edwin McCravy(20055) (Show Source): You can put this solution on YOUR website!
Three men can individually do a job in 5, 6 and 7 hours respectively. What is the greatest fractional part of the job that can be done in 2 hours by any two of the men working together?


Obviously the greatest fractional part will be done by the two fastest workers,
so we can ignore the slowest worker, the one who takes 7 hours.

The first man can do 1 job in 5 hours, so his rate in jobs/hour is 

 or 

The second man can do 1 job in 6 hours, so his rate in jobs/hour is 

 or 

When the first and second men work together, their combined rate is
 =  = .  So in 2 hours they can do twice job
which is job.  That reduces to  of a job.

Answer .

Edwin

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