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If Elon and Jeff work together, they can finish the work in 3 hours. If Jeff works together with Bruce, they

can make this work done in 6 hours. Elon and Bruce can finish this work in 4 hours. How much time would
it take to finish the work if all three worked together? pls helpp

1 Answer

4 votes

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
User Suresh Palemoni
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