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July 20th, 2014, 05:42 AM   #1
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In how many hours will the three of them complete the job working together?

A piece of work is to be completed by P, Q and R. P can finish the job in 8 hours, Q in 40 hours and R in 20 hours. In how many hours will the three of them complete the job working together?

Since the three people involved are working at different rates/hours, it would be untrue to say that the total time the people would finish the work =
8+40+20=68 hours


Let look at it this way, since it takes the people involved different duration to finish the same work, let's find how much work each of them does in an hour.

In one hour:
P does 1/8 of the job.
Q does 1/40 of the job.
R does 1/20 of the job.

The total fraction of the job done by the people involved in an hour =
1/8 + 1/40 + 1/20
= 1/5

The problem now is how to determine how long it would take them to finish the job if they are doing the same job together.
Who may help me here?

Last edited by Chikis; July 20th, 2014 at 05:47 AM.
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July 20th, 2014, 08:18 AM   #2
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Shouldn't it be 5 hours? Since 1/5 of the job is done in an hour, 5*1/5=1

I'm not really sure because this seems kind of easy to be the answer :P
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July 20th, 2014, 08:22 AM   #3
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In case you're serious:
1/5 of job takes 1 hour;
5/5 of job takes 5 hours.
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July 20th, 2014, 11:24 AM   #4
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Thank you. I think I undestand what you mean.
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