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# A takes 24 hours to finish a job, B takes 18 hours. If they

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Senior Manager
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A takes 24 hours to finish a job, B takes 18 hours. If they [#permalink]

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27 Nov 2004, 16:38
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A takes 24 hours to finish a job, B takes 18 hours. If they work together, what fraction of the job is left at the end of 8 hours?
Manager
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28 Nov 2004, 01:47
It takes A & B, working together, 1/(1/24 + 1/18) = 72/7 hours to complete the job.
If they've already worked 8 hours then 72/7 - 8 = 9/7 hour is the time remaining to finish the job.
That is equivalent to saying
(9/7)/(72/7) = 1/8 is the fraction of the job left at the end of 8 hours.
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28 Nov 2004, 05:20
2/9

In 72/7 hrs they complete the whole job, so in 8 hrs they complete 7/9, so what's remaining is 2/9
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28 Nov 2004, 15:37
I'm getting 2/9

A&B combined can get the job X done in 72/7 hrs
In 8 hrs A&B can get: 8/(72/7) * X done = 7/9 * X

Job left = 2/9 of X

-fm
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29 Nov 2004, 05:20
I'm getting 2/9 as well:

A, after 8 hours finishes 8/24 = 1/3 of the job
B, after 8 hours finishes 8/18 = 4/9 of the job

Job done by A + job done by B = (1/3) + (4/9) = 7/9

>>> Job left: 1 - 7/9 = 2/9
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Manager
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29 Nov 2004, 13:11
oxon wrote:
It takes A & B, working together, 1/(1/24 + 1/18) = 72/7 hours to complete the job.
If they've already worked 8 hours then 72/7 - 8 = 9/7 hour is the time remaining to finish the job.
That is equivalent to saying
(9/7)/(72/7) = 1/8 is the fraction of the job left at the end of 8 hours.

72/7 - 8 = 72/7 - 56/7 = 16/7, not 9/7

so (16/7)/(72/7) = 16/72 = 4/18 = 2/9

I think the answer is 2/9
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29 Nov 2004, 14:02
agree. 2/9

they take 72/7 hours to do the job. in 8 hours, they complete 7/9 part. hence, 2/9 is left.
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29 Nov 2004, 14:02
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