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Bunuel
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Machine x takes 4 hours to complete a job and machine y takes 5 hours 13 Jan 2021, 02:00
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25% (medium)

Question Stats:

79% (01:46) correct 21% (02:15) wrong based on 268 sessions

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Machine x takes 4 hours to complete a job and machine y takes 5 hours to complete the same job. Machine x works alone and completes one-half the job, and then machine x and y together complete the job. How long does it take for the entire job to be completed?

A. 10/9
B. 26/9
C. 3
D. 28/9
E. 29/9
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D
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Machine x takes 4 hours to complete a job and machine y takes 5 hours 13 Jan 2021, 04:24
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Complete Job by Machine X take 4 hours. Therefore half the job takes 2 hours.

Work done by X and Y together in 1 hour = 1/4 + 1/5 = 9/20.

Therefore time taken to complete it together = 20/9 hours

Time taken to do half the job together = 10/9 hours

Total time taken = 2 + 10/9 = 28/9 hours


Option D

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Machine x takes 4 hours to complete a job and machine y takes 5 hours 14 Jan 2021, 01:47
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Using efficiency, the time taken to complete the work is \(\frac{28}{9}\)

Ans D
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Machine x takes 4 hours to complete a job and machine y takes 5 hours 14 Jan 2021, 03:34
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Bunuel
Machine x takes 4 hours to complete a job and machine y takes 5 hours to complete the same job. Machine x works alone and completes one-half the job, and then machine x and y together complete the job. How long does it take for the entire job to be completed?

A. 10/9
B. 26/9
C. 3
D. 28/9
E. 29/9
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Combined rate of work = 1/4 + 1/5 = 9/20

Once half the work is done in 2 hrs by machine x, the leftover work = 1/2

Time taken = Work/Rate = (1/2)/(9/20) = 10/9 hrs

Total time taken = 2 hrs + 10/9 hrs = 28/9 hrs

Answer (D)
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Machine x takes 4 hours to complete a job and machine y takes 5 hours 20 Jan 2021, 02:30
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Bunuel
Machine x takes 4 hours to complete a job and machine y takes 5 hours to complete the same job. Machine x works alone and completes one-half the job, and then machine x and y together complete the job. How long does it take for the entire job to be completed?

A. 10/9
B. 26/9
C. 3
D. 28/9
E. 29/9
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Veritas Prep Official Explanation



Rate x = 1/4 and Rate y = 1/5 and Rate combined = 9/20. First calculate how long it takes machine x to do half the job using logic (if 4 hrs to do the whole job, then 2 hrs to do half) or the W = RT formula: 1/2 = 1/4 x T, so T = 2. Then calculate how long it takes them together to do the second half of the job: 1/2 = 9/20 x T, so T = 10/9 . Therefore in took 2 + 10/9 or 28/9 hours to complete the whole job.
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Machine x takes 4 hours to complete a job and machine y takes 5 hours 11 Sep 2025, 14:17
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