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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, 11:16

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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

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

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;

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

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31 Jul 2013, 12:05

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.

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

Anybody please explain

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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29 Mar 2014, 03:58

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

Rgds, TGC!
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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, 03:03

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.

Answer: C.

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

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.

Answer: C.

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.
_________________

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

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24 Dec 2016, 03:09

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

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24 Dec 2016, 17:29

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

if all 3 work all 10 hours, then work ratio of fastest to slowest is 10*3/10*1=3/1 but slowest worked only 6 hours, so ratio is 10*3/6*1=5/1 C

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

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12 Mar 2017, 11:01

Let's ignore the middle worker: Productivity ratio: 1:3 1-4 hours slowest did 4 quickest did 3*4 10 hours: slowest did 4+2, quickest did 3*10 Hence the work ratio is 6:30 the fastest to slowest is 30:6 or 5:1, hence, C

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

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13 Mar 2017, 10:31

Bunuel wrote:

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

Anybody please explain

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.

Hey Bunnel, I actually solved it right except I made a quite a silly mistake. When it says the job takes 10 hours to do, does it include the 10th hour? so would it be 9 full hours or 10 full hours for the work done? this was confusing so i had 30\7

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

1. (time worked by slowest worker)/ (time taken by slowest worker working alone) +(time worked by fastest worker)/ (time taken by fastest worker workign alone)+(time worked by third worker)/ (time taken by third worker working alone) 2. (4+2)/3x + 10/x + 10/2x=1 3. Ratio of work performed by fastest to slowest is (10/x)/(6/3x)=5 to 1

Note: Time taken when working alone is given by the productivity.
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