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3 machines have a productivity ratio of 1 to 2 to 5. All 3 [#permalink]

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16 Feb 2011, 04:34

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3 machines have a productivity ratio of 1 to 2 to 5. All 3 machines are working on a job for 3 hours. At the beginning of the 4th hour, the slowest machine breaks. It is fixed at the beginning of hour seven, and begins working again. The job is done in nine hours. What was the ratio of the work performed by the fastest machine as compared to the slowest?

3 machines have a productivity ratio of 1:2:5. all 3 machines are working on a job for 3 hours. at the beginning of the 4th hour, the slowest machine breaks. it is fixed at the beginning at hour 7, and begins working again. the job is done in 9 hours. what was the ratio of the work performed by the fastest machine to the work performed by the slowest?

"3 machines have a productivity ratio of 1:2:5" means that in a time interval (1 hour, 1 year, ...) the first machine can produce 1 part (so it's the slowest one), the second can produce 2 parts and the third and fastest one can produce 5 parts.

Now, the fastest machine worked for whole 9 hours thus produced 9*5=45 parts but the slowest machine worked only for 6 hours thus produced 6*1=6 parts, so the ratio of the work performed by the fastest machine to the work performed by the slowest is 45/6=15/2.
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Re: 3 machines have a productivity ratio of 1 to 2 to 5. All 3 [#permalink]

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11 Aug 2011, 06:02

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ruturaj wrote:

please explain how slowest machine works for 6 hours

slowest machine worked 1st hour 2nd hour 3rd hour Got broken got fixed and returned to work at the beginning of the 7th hour so: 7th hour 8th hour 9th hour

Total of 6 hours.

So the slowest machine made 6 pieces, while the fastest machine made 45
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Re: 3 machines have a productivity ratio of 1 to 2 to 5. All 3 [#permalink]

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05 Jan 2017, 17:19

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GMATD11 wrote:

3 machines have a productivity ratio of 1 to 2 to 5. All 3 machines are working on a job for 3 hours. At the beginning of the 4th hour, the slowest machine breaks. It is fixed at the beginning of hour seven, and begins working again. The job is done in nine hours. What was the ratio of the work performed by the fastest machine as compared to the slowest?

A. 5 B 7 C 15/2 D 17/2 E 12

fastest machine's work=9hrs*5 units per hr=45 total units slowest machine's work=6 hrs*1 unit per hr=6 total units 45/6=15/2

Re: 3 machines have a productivity ratio of 1 to 2 to 5. All 3 [#permalink]

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11 Aug 2011, 08:02

ruturaj wrote:

please explain how slowest machine works for 6 hours

3 machines have a productivity ratio of 1:2:5. all 3 machines are working on a job for 3 hours. at the beginning of the 4th hour, the slowest machine breaks. it is fixed at the beginning at hour 7, and begins working again. the job is done in 9 hours. what was the ratio of the work performed by the fastest machine to the work performed by the slowest?

Productivity ratio of 1:2:5 means;

In 1 hour: Slowest machine just finishes 1 work Medium fast machine finishes 2 work Fastest machine finishes 5 work

3 hours work: Slowest: 3*1=3 work Medium: 3*2=6 work Fastest: 3*5=15 work

THEN SLOWEST BREAKS. It misses(3 hours): 4th hour 5th hour 6th hour

During which: Medium fast completes: 3*2=6 work Fastest completes: 3*5=15 work

Then 7th, 8th, 9th hour(3 hours) Slowest: 3*1=3 work Medium: 3*2=6 work Fastest: 3*5=15 work

Work by fastest:Work by slowest 15+15+15:3+3 45:6 15:2 _________________

Re: 3 machines have a productivity ratio of 1 to 2 to 5. All 3 [#permalink]

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02 Dec 2012, 22:49

The productivity ratio of the fastest machine to the slowest machine is 5:1.

The fastest machine worked for 9 straight hours. Thus, W = 5 x 9 = 45 The slowest machine brokedown in the 4th hour and was revived on the 7th hour. Thus, W = 1 x 6 = 6

The Output Ratio of fastest to slowest is 45 is to 6 ==> 15 : 2
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Re: 3 machines have a productivity ratio of 1 to 2 to 5. All 3 [#permalink]

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05 Jan 2017, 15:19

Let's say the productivity ratio refers to how many units each produces in 1 hour. The fastest (most productive) machine works for 9 hours and makes 5 per hour, totally 45 units. The slowest (least productive) machine works for 6 hours and produces 1 per hour for a total of 6. Thus, the ratio of units produced fast/slow is 45/6 or 15/2. No more math required
_________________

Dan the GMAT Man Offering tutoring and admissions consulting in the NYC area and online danthegmatman.squarespace.com danthegmatman@gmail.com

3 machines have a productivity ratio of 1 to 2 to 5. All 3 [#permalink]

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09 Apr 2017, 14:25

Common sense solution:

Ratio of work is 1:2:5

Meaning: As Bunuel defined "in a time interval (1 hour, 1 year, ...) the first machine can produce 1 part (so it's the slowest one), the second can produce 2 parts and the third and fastest one can produce 5 parts."

Time progression:

Hour 1: 1:2:5 parts produced Hour 2: 2:4:10 parts produced Hour 3: 3:6:15 parts produced Hour 4: 3:8:20 parts produced //Machine 1 breaks, produces no more parts Hour 5: 3:10:25 parts produced Hour 6: 3:12:30 parts produced Hour 7: 4:14:35 parts produced //Machine 1 is fixed, continues to produce parts Hour 8: 5:16:40 parts produced Hour 9: 6:18:45 parts produced //Job done

So when looking at the final tally of parts produced in 9 hours, the fastest machine produced 45 parts and the slowest produced only 6. Reducing this ratio we get 15/2.

Re: 3 machines have a productivity ratio of 1 to 2 to 5. All 3 [#permalink]

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12 Apr 2017, 09:55

The productivity ratios are 1:2:5. Let's assume that the basic rate is x. So rates are 1x:2x:5x. The fastes machine worked 9 hours, therefore it did 9/1x work. The slowest machine didn't work from 4th to 6th hours so were broken for 3 hours. Therefore the work done by this machine is 6/5x. Let's compare work done by both machines: (9/1x)/(6/5x)=(9/x)*(5x/6)=15/2