Question

Charles can do a job in 1 hour, bill can do the same job in 2 hours, and bob can do the job in 3 hours. How long does it take them to do the job working together?

Answer 1

Charles can do the whole job in an hour, Bill can do 1/2 of the job in an hour, and Bob does 1/3 of the job in an hour.  Therefore, they do a total of 1+1/2+1/3=11/6 of the job in an hour, meaning it takes them 6/11 of an hour.  This is 6/11*60=360/11 minutes, or approximately 33 minutes.

Answer 2

Charles does a complete job in 1 hour.
Bill does 1/2 of a job in an hour.
Bob does 1/3 of a job in an hour.

If they're all working on the same job, or copies of the same one,
then working together, they do (1 + 1/2 + 1/3) job per hour.

(1) + (1/2) + (1/3) = (6/6) + (3/6) + (2/6) = 11/6 job/hour

Working at the rate of 11/6 job per hour, the team needs 6/11 hour per job.

6/11 hour is 32 minutes 43-21/33 seconds .