Three workers have a productivity ratio of 1 to 2 to 3. All : GMAT Problem Solving (PS)
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# Three workers have a productivity ratio of 1 to 2 to 3. All

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Three workers have a productivity ratio of 1 to 2 to 3. All [#permalink]

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01 Jun 2012, 10:16
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The Book does not show any answers. Hence I need to figure out if I have done them correctly or not. Please help me if you can. Would greatly appropriate it. Thanks

Three workers have a productivity ratio of 1 to 2 to 3. All three workers are working on a job for 4 hours. At the beginning of the 5th hour, the slowest worker takes a break. The slowest worker comes back to work at the beginning of the 9th hour and begins working again. The job is done in ten hours. What was the ratio of the work performed by the fastest worker as compared to the slowest?

A. 12 to 1
B. 6 to 1
C. 5 to 1
D. 1 to 6
E. 1 to 5
[Reveal] Spoiler: OA
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01 Jun 2012, 18:44
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I got to (C)

Ratio Setup 1:2:3, I ignored 2 as the question only asked for comparison between the slowest and fastest so it becomes 1:3. They each worked for (4) hours until the slowest took a break so the 4th hour ratio would look like

4th hour -4:12
5th hour - 4:15 (slowest worker takes a break until the 9th hour)
6th hour - 4:18
7th hour - 4:21
8th hour - 4:24
9th hour - 5:27
10th hour - 6:30 = 1 to 5 ratio.

1 to 5 ratio slowest compared to fastest

flip it around as it is asking for a fastest to slowest comparison so it becomes 5 to 1.
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Re: Three workers have a productivity ratio of 1 to 2 to 3. All [#permalink]

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02 Jun 2012, 06:23
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phoenix9801 wrote:
The Book does not show any answers. Hence I need to figure out if I have done them correctly or not. Please help me if you can. Would greatly appropriate it. Thanks

Three workers have a productivity ratio of 1 to 2 to 3. All three workers are working on a job for 4 hours. At the beginning of the 5th hour, the slowest worker takes a break. The slowest worker comes back to work at the beginning of the 9th hour and begins working again. The job is done in ten hours. What was the ratio of the work performed by the fastest worker as compared to the slowest?

A. 12 to 1
B. 6 to 1
C. 5 to 1
D. 1 to 6
E. 1 to 5

The fastest worker who does 3 units of job worked for all 10 hours, so he did 3*10=30 units of job;

The slowest worker who does 1 unit of job worked for only 4+2=6 hours (first 4 hours and last 2 hours), so he did 1*6=6 units of job;

The ratio thus is 30 to 6, or 5 to 1.

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

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30 Jul 2013, 08:04
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Bumping for review and further discussion.
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Re: Three workers have a productivity ratio of 1 to 2 to 3. All [#permalink]

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31 Jul 2013, 11:05
This is a nice problem because it offers the chance to quite easily intuitively solve a problem. Maybe @Bunuel can go into detail how to systematically solve this problem and problems like it (i.e., problems like it that are much harder)? Here's how to use intuition though:

Ratio is 1:2:3 for slow:medium:fast.

Medium and fast each work for 10 hours, while slow works for 6 hours because he skipped 4 hours.

So in 10 hours, fast does 30 units if work, and in 10 hours, medium does 20 units of work, while in 6 hours, slow does 6 units of work.

So, the job required 56 units of work, 30 of which were done by fast and 6 of which were done by slow. so 30 to 6 = 5 to 1.

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

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06 Aug 2013, 01:14
Let A, B, C be the rates of the slowest to the fastest workers, respectively. --> C = 3A

A worked for 6 hours since he skipped 4 hours from the 5th to the 8th while C worked for 10 hours. --> Total work of A = 6A and total work of C = 10C

Work C/Work A = 10C/6A= (10*3A)/6A = 5/1 --> C.
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Re: Three workers have a productivity ratio of 1 to 2 to 3. All [#permalink]

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27 Oct 2013, 23:56
Hello,

Could anyone just help me interpret "productivity ratio of 1 to 2 to 3"

I could come to conclusion that for first worker rate is 3 units of work per hour.

Also what would the rate for other two(B & C) workers

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

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28 Oct 2013, 00:18
bsahil wrote:
Hello,

Could anyone just help me interpret "productivity ratio of 1 to 2 to 3"

I could come to conclusion that for first worker rate is 3 units of work per hour.

Also what would the rate for other two(B & C) workers

Three workers have a productivity ratio of 1 to 2 to 3, means that if A does 1 unit of work in an hour, then B does 2 and C does 3. A's rate in this case is 1 unit/hour, B's 1/2 unit/hour and C's 1/3 unit/hour.
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Re: Three workers have a productivity ratio of 1 to 2 to 3. All [#permalink]

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28 Oct 2013, 00:22
Productivity ratio 1:2:3 (for ex: A:B:C) is B is twice as much productive as A & C is thrice as much productive as A

So, between A, B & C, A is least productive & C is most productive.

As far as B:C is concerned, it will still be 2:3
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Re: Three workers have a productivity ratio of 1 to 2 to 3. All [#permalink]

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29 Mar 2014, 02:58
Another Approach:

More the productivity More the rate. Hence,

1:2:3

Consider X,2x, and 3x where person having rate x is slowest and person having rate 3x is fastest.

All of them work for 6 hours in total 10 hours. Then,

x+2x+3x = 6x Rate

Rate * Time = Work
6x * 6 = 36x

And 3x+2x=5x (Both of the other two work for extra 4 hours in 10 hours)

5x * 4 = 20x

Total work = 20x + 36x = 56x

Fastest worker does work for 10 hours hence Work(Fast) = 30x
Slowest worker does work for 6 hours hence Work(Slow) = 6x

Ratio = 30/6 = 5/1

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

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16 May 2014, 02:03
Bunuel wrote:
phoenix9801 wrote:
The Book does not show any answers. Hence I need to figure out if I have done them correctly or not. Please help me if you can. Would greatly appropriate it. Thanks

Three workers have a productivity ratio of 1 to 2 to 3. All three workers are working on a job for 4 hours. At the beginning of the 5th hour, the slowest worker takes a break. The slowest worker comes back to work at the beginning of the 9th hour and begins working again. The job is done in ten hours. What was the ratio of the work performed by the fastest worker as compared to the slowest?

A. 12 to 1
B. 6 to 1
C. 5 to 1
D. 1 to 6
E. 1 to 5

The fastest worker who does 3 units of job worked for all 10 hours, so he did 3*10=30 units of job;

The slowest worker who does 1 unit of job worked for only 4+2=6 hours (first 4 hours and last 2 hours), so he did 1*6=6 units of job;

The ratio thus is 30 to 6, or 5 to 1.

Hi Bunuel you say that the slowest worker worked for 4+2=6 hours( first 4 hours and last 2 hours) should it not be 5+1=6 since the question says that the slowest worker takes a break at the beginning of the fifth hour which means he has worked for 5 hours and also he joins back at the beginning of the 9th hour and the work completes in 10 hours which means after joining he worked only for an hour? please correct me if i am wrong
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Re: Three workers have a productivity ratio of 1 to 2 to 3. All [#permalink]

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16 May 2014, 02:14
havoc7860 wrote:
Bunuel wrote:
phoenix9801 wrote:
The Book does not show any answers. Hence I need to figure out if I have done them correctly or not. Please help me if you can. Would greatly appropriate it. Thanks

Three workers have a productivity ratio of 1 to 2 to 3. All three workers are working on a job for 4 hours. At the beginning of the 5th hour, the slowest worker takes a break. The slowest worker comes back to work at the beginning of the 9th hour and begins working again. The job is done in ten hours. What was the ratio of the work performed by the fastest worker as compared to the slowest?

A. 12 to 1
B. 6 to 1
C. 5 to 1
D. 1 to 6
E. 1 to 5

The fastest worker who does 3 units of job worked for all 10 hours, so he did 3*10=30 units of job;

The slowest worker who does 1 unit of job worked for only 4+2=6 hours (first 4 hours and last 2 hours), so he did 1*6=6 units of job;

The ratio thus is 30 to 6, or 5 to 1.

Hi Bunuel you say that the slowest worker worked for 4+2=6 hours( first 4 hours and last 2 hours) should it not be 5+1=6 since the question says that the slowest worker takes a break at the beginning of the fifth hour which means he has worked for 5 hours and also he joins back at the beginning of the 9th hour and the work completes in 10 hours which means after joining he worked only for an hour? please correct me if i am wrong

No.

At the beginning of the 5th hour, the slowest worker takes a break, means that this worker worked only for the first 4 hours (he left when 5th hour started).

The slowest worker comes back to work at the beginning of the 9th hour and begins working again, means that this worker worked for 9th hour.
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Re: Three workers have a productivity ratio of 1 to 2 to 3. All [#permalink]

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02 Nov 2015, 05:55
R*T = W

Slow - 1/3w/h
Fast - 1w/h

1/3*4+1/3*2=4/3+2/3=6/3=2

1*4+1*4+1*2=10

10:2=5:1

C
Re: Three workers have a productivity ratio of 1 to 2 to 3. All   [#permalink] 02 Nov 2015, 05:55
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