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Little work problem help please

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Little work problem help please [#permalink] New post 14 Aug 2003, 04:21
I know this one has been posted before, but could someone take me through the steps to get the answer.


Working together, A and B can do a job in 6 days. B and C can do the same job in 10 days, while C and A can do it in 7.5 days. How long will it take if all A, B and C work together to complete the job?

A. 8 days
B. 5 days
C. 3 days
D. 7days

This is new, but is this correct?

3 workers together take 18 hours to complete a job. If a worker is added, who works at the same rate, how long will it take the four of them to complete the job? Second if 3 workers take 18 hours to complete the job, how long will it take 2 workers to do the job if one leaves due to disability?

would the first part be 13.5 hours and the second part be 27 hours?

Thanks again,

Rich
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First Part [#permalink] New post 14 Aug 2003, 06:24
Rich,

Here is the solution to the first part...

set up the three equations:

1/A + 1/B = 1/6
1/B + 1/C = 1/10
1/C + 1/A = 1/7.5

Now add all three equations together (the right side can be tricky b/c of finding the LCD, I used 60, turns out 30 would have worked all the same)

You get...

2/A + 2/B + 2/C = 24/60
now divide both sides by 2 to get what you are looking for...

1/A + 1/B + 1/C = 24/120

So the answer is the reciprocal (do you see why?) = 120/24 = 5 hrs
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Thank You [#permalink] New post 14 Aug 2003, 06:27
I forgot to get the lcd and just added them-dumb mistake,

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Part 2 [#permalink] New post 14 Aug 2003, 06:29
For the second part you are correct, but you seem unsure of your answer. I will explain.

If three workers acan do this job together in 18 hrs, they they each take 54 hrs to do it alone.
So the answer to the first part is 4/54 = 1/x = 54/4 = 13.5.

And the second is just 2/54 = 1/x = 54/2 = 27.

Good joob Rich, you had the intuition - next will come the confidence!! :-D
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Thanks again [#permalink] New post 14 Aug 2003, 06:31
I had a lot of these last week on the test. I'll ace it next time.

Thanks,

Rich
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[#permalink] New post 14 Aug 2003, 07:01
Rich,

You say that you had a few of these on the REAL GMAT? How complicated did they get? Can you change some data and provide examples?

thanks man
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 [#permalink] New post 14 Aug 2003, 07:11
Nothing hard for you guys. What I saw was pretty much like my first post where you have x workers and one leaves/ or is added and you have to figure out how long the job will take. I'm kicking myself for not buying the Kaplan 800 book because some of the hard problems I missed are concepts that are covered in that book.
  [#permalink] 14 Aug 2003, 07:11
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