Answer:
2 2/3 hours
Explanation:
You want to know the time it would take Elon, Jeff, and Bruce working together, if Elon and Jeff can complete the work in 3 hours, Jeff and Bruce take 6 hours, and Elon and Bruce take 4 hours.
Total of rates
Job completion time problems like this one are more easily understood in terms of rate of completion. If we let e, j, and b represent the rates of job completion in jobs per hour for each of Elon, Jeff, and Bruce, respectively, then the given relations can be written ...
e +j = 1/3
j +b = 1/6
e +b = 1/4
Adding these equations together gives ...
(e +j) +(j +b) +(e +b) = (1/3) +(1/6) +(1/4)
2(e +j +b) = 3/4 . . . . . . . simplify
e + j + b = 3/8 . . . . . . . . divide by 2
The total rate of job completion when Elon, Jeff, and Bruce work together is 3/8 job per hour. The hours it takes them to do one job is the reciprocal of this:
1/(3/8 job/hour) = 8/3 hour/job
It would take Elon, Jeff, and Bruce 2 2/3 hours to complete the work if they worked together.
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Additional comment
For this problem, we don't need to know the individual completion times. If we were to figure them we'd find them to be (working alone) ...
- Elon: 4.8 hours
- Jeff: 8 hours
- Bruce: 24 hours