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for a certain job,A and B together worked for 6/5 hours, B [#permalink]

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18 Sep 2003, 12:44

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for a certain job,A and B together worked for 6/5 hours,
B and C worked for3/2 hours, A and C worked for 2 hours. If all of
them work simultaneously, how many hours can this job be done?

for a certain job,A and B together worked for 6/5 hours, B and C worked for3/2 hours, A and C worked for 2 hours. If all of them work simultaneously, how many hours can this job be done?

Not sure if this is the best explanation, but I will try...

In one hour A and B together can finish 5/6 of the job
In one hour B and C together can finish 2/3 of the job
In one hour C and A together can finish 1/2 of the job

So, if we add all these up:

In one hour 2 A's, 2 B's and 2 C's can finish (5/6 + 2/3 + 1/2) = 2 times the job.

So, A, B and C can finish the job in 1 hour.

Praet, is this answer correct. For the benefit of everyone, maybe you can explain the answer better than I did. Thanks.

(A+B) + (B+C) + (C+A) = 6/5+3/2+2 = 47/10
In this time 3 times work is done
2A+2B+2C will do one job in 47/30 hours
so
A+B+C will need 47/60 hrs to do one job, working together

I interpret the question the same way that you do-- and I think your approach is right.

But 47 minutes is an ugly answer. I bet calnhob has interpreted the syntax correctlyand is right, just by the simplicity of his answer.

And also, since we've hijacked the board today, and are doing more chatting than GMAT work, I'd like to note that I wonder how Paul is doing on his test...

(A+B) + (B+C) + (C+A) = 6/5+3/2+2 = 47/10 In this time 3 times work is done 2A+2B+2C will do one job in 47/30 hours so A+B+C will need 47/60 hrs to do one job, working together

Thus they need 47 minutes to complete one job.

Hey Anand,

I do not see any difference between yours and calnhob's way of interpreting this problem.

Looking at your logic, I believe that you also considered that

A and B together took 6/5 hours to complete the ENTIRE job.
B and C together took 3/2 hours to complete the ENTIRE job.
A and C together took 2 hours to complete the ENTIRE job.

This is the same way in which calnhob interpreted the problem. But I think he applied the right formula.

So your statement "In 47/10 hours the work is completed 3 times is correct" (If each pair works once and finishes the entire job)

However, I think it is not correct to say that

If 2A + 2B + 2C can complete 3 times a job in 47/10 minutes, it will take 47/30 minutes to complete the job once. The proportionality can not be applied here because everybody has different rate of working. Here the effeciency factor comes in to play. (consider a simple example where all the players work with a different rates and it will be more clear)

In my opinion, the work related problems can not be solved by applying the straight formula. Because the longer one takes to finish a job, he lesser is the amount of work that can be finished in unit time.