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If a group of 5 craftsmen takes 3 hours to finish a job

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If a group of 5 craftsmen takes 3 hours to finish a job  [#permalink]

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New post 10 Mar 2017, 22:40
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If a group of 5 craftsmen takes 3 hours to finish a job, how long will it take a group of 4 apprentices to do the same job?

(1) An apprentice works at 2/3 the rate of a craftsman.

(2) The 5 craftsmen and the 4 apprentices working together will take 45/23 hours to finish the job

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Re: If a group of 5 craftsmen takes 3 hours to finish a job  [#permalink]

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New post 11 Mar 2017, 00:13
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HKD1710 wrote:
If a group of 5 craftsmen takes 3 hours to finish a job, how long will it take a group of 4 apprentices to do the same job?

(1) An apprentice works at 2/3 the rate of a craftsman.

(2) The 5 craftsmen and the 4 apprentices working together will take 45/23 hours to finish the job


I figured D.

1- An apprentice works at 2/3 the rate of a craftsman.

5 craftsmen finish work in 3 hours.
--> 1 craftsman does the job in \(= 5x3 = 15h\)
--> 1 apprentice = 2/3 craftsman
--> time by 1 apprentice will hence be reciprocal \(=15 x 3/2 = 45/2 = 22.5\)
--> time by 4 apprentices \(= 22.5/4 = 5.625\)

1 is -- clearly sufficient.

2- I kind of figured there is just one variable unknown which is the time taken by apprentices alone. We have rate of work of craftsmen and craftsmen + apprentices combined. One variable can be easily found. I actually found this question on a quick search, solved a few years ago.

https://gmatclub.com/forum/work-word-pr ... ml#p843620
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Re: If a group of 5 craftsmen takes 3 hours to finish a job  [#permalink]

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New post 21 Feb 2020, 12:04
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Re: If a group of 5 craftsmen takes 3 hours to finish a job  [#permalink]

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New post 24 Feb 2020, 00:40
HKD1710 wrote:
If a group of 5 craftsmen takes 3 hours to finish a job, how long will it take a group of 4 apprentices to do the same job?

(1) An apprentice works at 2/3 the rate of a craftsman.

(2) The 5 craftsmen and the 4 apprentices working together will take 45/23 hours to finish the job


Time, rate and job in work problems are in the same relationship as time, speed (rate) and distance in rate problems.

\(time*speed=distance\) <--> \(time*rate=job \ done\).

So, if we say that the rate of a craftsmen is \(x\) job/hours and the rate of an apprentice is \(y\) job/hour then we'll have \((5x)*3=job=(4y)*t\) --> \((5x)*3=(4y)*t\). Question: \(t=\frac{15x}{4y}=?\)

(1) Each apprentice works at 2/3 the rate of a craftsman --> \(y=\frac{2}{3}x\) --> \(\frac{x}{y}=\frac{3}{2}\) --> \(t=\frac{15x}{4y}=\frac{45}{8}\) hours. Sufficient.

(2) The 5 craftsmen and the 4 apprentices working together will take 45/23 hours to finish the job --> as the 5 craftsmen need 3 hours to do the job then in 45/23 hours they'll complete (45/23)/3=15/23 rd of the job (15 parts out of 23) so the rest of the job, or 1-15/23=8/23 (8 parts out of 23) is done by the 4 apprentices in the same amount of time (45/23 hours): \(\frac{5x}{4y}=\frac{15}{8}\) --> \(\frac{x}{y}=\frac{3}{2}\), the same info as above. Sufficient.

Answer: D.
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Re: If a group of 5 craftsmen takes 3 hours to finish a job   [#permalink] 24 Feb 2020, 00:40
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