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# 'Work' Word Problems Made Easy

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11 Aug 2013, 00:09
Hi,

Can sombody please solve this wit solution for this question.

It takes Printer A 4 more minutes than printer B to print 40 pages. Working together, the two printers can print 50 pages in 6 minutes. how long will it take printer A to print 80 pages?
a. 12 b. 18 c. 20 d. 24 e. 30

Regards,
Rrsnathan.
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11 Aug 2013, 00:14
rrsnathan wrote:
Hi,

Can sombody please solve this wit solution for this question.

It takes Printer A 4 more minutes than printer B to print 40 pages. Working together, the two printers can print 50 pages in 6 minutes. how long will it take printer A to print 80 pages?
a. 12 b. 18 c. 20 d. 24 e. 30

Regards,
Rrsnathan.

Check here: it-takes-printer-a-4-more-minutes-than-printer-b-to-print-98479.html

Hope it helps.
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02 Sep 2013, 12:18
Just 3 hours back, literally I was at zero confidence to start with work rate problems, but after going through your notes and solving 5 or 6 problems, I have solved 80 to 90% difficulty level problems like a pro, solutions are also matching closely to Bunuel's. Really work rate is not that as much tough as I was thinking before. Reciprocate the hours to find the rate of work per day or per minute that's it half battle won-> "master key to every work rate problem".

Thanks allot.
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16 Sep 2013, 22:46
Bunuel wrote:
resh924 wrote:
Bunuel,

Can you help me with this question?

A group of 5 craftsmen, working together at the same rate, can finish a job in 3 hours. How long will it take a group of 4 apprentices working together to do the same job?
(1) Each 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.

Answer choice seems to be D.

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.

Hi Bunuel,

For #2, I set-up my equation as:

1/3 + 1/A = 1/(45/23)

Since we already know the rate of the 5 craftsmen and the total hours needed for the 2 groups to finish the job. However, I arrived at a different answer for A (45/8). I can't seem to figure out where it went wrong, hope you can help.

Thanks.
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16 Sep 2013, 23:43
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pauc wrote:
Bunuel wrote:
resh924 wrote:
Bunuel,

Can you help me with this question?

A group of 5 craftsmen, working together at the same rate, can finish a job in 3 hours. How long will it take a group of 4 apprentices working together to do the same job?
(1) Each 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.

Answer choice seems to be D.

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.

Hi Bunuel,

For #2, I set-up my equation as:

1/3 + 1/A = 1/(45/23)

Since we already know the rate of the 5 craftsmen and the total hours needed for the 2 groups to finish the job. However, I arrived at a different answer for A (45/8). I can't seem to figure out where it went wrong, hope you can help.

Thanks.

You should get the same answer: 1/3 + 1/A = 1/(45/23) --> A=45/8.
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17 Sep 2013, 02:31
Quote:
Hi Bunuel,

For #2, I set-up my equation as:

1/3 + 1/A = 1/(45/23)

Since we already know the rate of the 5 craftsmen and the total hours needed for the 2 groups to finish the job. However, I arrived at a different answer for A (45/8). I can't seem to figure out where it went wrong, hope you can help.

Thanks.

You should get the same answer: 1/3 + 1/A = 1/(45/23) --> A=45/8.[/quote]

Oops, you're right. I was obsessing over a different value (3/2 from Statement 2). Thank you.
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25 Jul 2014, 17:23
Bunuel wrote:
resh924 wrote:
Bunuel,

Can you help me with this question?

A group of 5 craftsmen, working together at the same rate, can finish a job in 3 hours. How long will it take a group of 4 apprentices working together to do the same job?
(1) Each 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.

Answer choice seems to be D.

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 andthe 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.

Check this for more: word-translations-rates-work-104208.html

Bunuel,

I agree with the answer you got but not the logic you used to arrive at the answer. The reason that I disagree with your logic is based on my understanding that DS questions are precise in their statements and we are not supposed to assume anything outside of what is stated. Can you please care to comment on the following?

Nowhere in the question stem it is mentioned that 4 apprentices work at the same rate. So, I am not sure if the highlighted portion in your solution is valid.

Statement 1: We can deduce that 4 apprentices work at the same rate since it says "Each apprentice works at 2/3 the rate of a craftsman"
For statement 2, we cannot assume that the 4 apprentices work at the same rate. However, since the question asks us to find time taken by group of 4 apprentices and not one apprentice, this statement alone can give us the answer and hence sufficient.

Is my understanding correct or am I reading too much into this?
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12 Oct 2014, 15:12
Example 3.
Working together, printer A and printer B would finish a task in 24 minutes. Printer A alone would finish the task in 60 minutes. How many pages does the task contain if printer B prints 5 pages a minute more than printer A?

Solution:
This problem is interesting because it tests not only our knowledge of the concept of word problems, but also our ability to ‘translate English to Math’

‘Working together, printer A and printer B would finish a task in 24 minutes’ This tells us that A and B combined would work at the rate of $$\frac{1}{24}$$ per minute.

‘Printer A alone would finish the task in 60 minutes’ This tells us that A works at a rate of $$\frac{1}{60}$$ per minute.

At this point, it should strike you that with just this much information, it is possible to calculate the rate at which B works: Rate at which B works = $$\frac{1}{24}-\frac{1}{60}=\frac{1}{40}$$.

[i]‘B prints 5 pages a minute more than printer A’[/i] This means that the difference between the amount of work B and A complete in one minute corresponds to 5 pages. So, let us calculate that difference. It will be $$\frac{1}{40}-\frac{1}{60}=\frac{1}{120}$$

‘How many pages does the task contain?’ If $$\frac{1}{120}$$ of the job consists of 5 pages, then the 1 job will consist of $$\frac{(5*1)}{\frac{1}{120}} = 600$$ pages.

Is there any other way to tackle this part. I am not able to understand it.
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12 Oct 2014, 23:04
earnit wrote:
Example 3.
Working together, printer A and printer B would finish a task in 24 minutes. Printer A alone would finish the task in 60 minutes. How many pages does the task contain if printer B prints 5 pages a minute more than printer A?

Solution:
This problem is interesting because it tests not only our knowledge of the concept of word problems, but also our ability to ‘translate English to Math’

‘Working together, printer A and printer B would finish a task in 24 minutes’ This tells us that A and B combined would work at the rate of $$\frac{1}{24}$$ per minute.

‘Printer A alone would finish the task in 60 minutes’ This tells us that A works at a rate of $$\frac{1}{60}$$ per minute.

At this point, it should strike you that with just this much information, it is possible to calculate the rate at which B works: Rate at which B works = $$\frac{1}{24}-\frac{1}{60}=\frac{1}{40}$$.

[i]‘B prints 5 pages a minute more than printer A’[/i] This means that the difference between the amount of work B and A complete in one minute corresponds to 5 pages. So, let us calculate that difference. It will be $$\frac{1}{40}-\frac{1}{60}=\frac{1}{120}$$

‘How many pages does the task contain?’ If $$\frac{1}{120}$$ of the job consists of 5 pages, then the 1 job will consist of $$\frac{(5*1)}{\frac{1}{120}} = 600$$ pages.

Is there any other way to tackle this part. I am not able to understand it.

Check here: working-together-printer-a-and-printer-b-would-finish-the-100221.html
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28 Oct 2014, 00:29
So I have a basic question:
Say we have three people:
A B C. A writes a page in 4 mins, B in 3 mins and C in 2 mins.
So how long will it take them to write 4 pages?

1/4 +1/3 +1/2 = 9/12. flip it to get 12/9= 3/4. so this is for a page (time taken).
3/4 * 4 =3 minutes.

My classfellow has been insisting we can just add up the time taken to get 9 minutes. for a page.
Is there any other way to do this question - except the way I did it.
I thought you could add up times when you're working on separate jobs. Not same job!
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10 Jan 2015, 23:13
Bunuel,

I have a question regarding Example 2.

Quote:
Example 2.
Working, independently X takes 12 hours to finish a certain work. He finishes 2/3 of the work. The rest of the work is finished by Y whose rate is 1/10 of X. In how much time does Y finish his work?

Solution:

‘Working, independently X takes 12 hours to finish a certain work’ This statement tells us that in one hour, X will finish 1/12 of the work.

‘He finishes 2/3 of the work’ This tells us that 1/3 of the work still remains.

‘The rest of the work is finished by Y whose rate is (1/10) of X’ Y has to complete of the work.

‘Y's rate is (1/10) that of X‘. We have already calculated rate at which X works to be . Therefore, rate at which Y works is .

‘In how much time does Y finish his work?’ If Y completes of the work in 1 hour, then he will complete of the work in 40 hours.

Why isn't the rate of work for X calculated as follows:

12hrs ---- 2/3 work
1 hr --- 1/18 work

Therefore, rate of work for Y should be (1/18)*(1/10) = (1/180).

1/180 work --- 1hr
1/3 work --- 180*(1/3) = 60hrs.

Thanks.
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11 Jan 2015, 10:58
asocialnot wrote:
Bunuel,

I have a question regarding Example 2.

Quote:
Example 2.
Working, independently X takes 12 hours to finish a certain work. He finishes 2/3 of the work. The rest of the work is finished by Y whose rate is 1/10 of X. In how much time does Y finish his work?

Solution:

‘Working, independently X takes 12 hours to finish a certain work’ This statement tells us that in one hour, X will finish 1/12 of the work.

‘He finishes 2/3 of the work’ This tells us that 1/3 of the work still remains.

‘The rest of the work is finished by Y whose rate is (1/10) of X’ Y has to complete of the work.

‘Y's rate is (1/10) that of X‘. We have already calculated rate at which X works to be . Therefore, rate at which Y works is .

‘In how much time does Y finish his work?’ If Y completes of the work in 1 hour, then he will complete of the work in 40 hours.

Why isn't the rate of work for X calculated as follows:

12hrs ---- 2/3 work
1 hr --- 1/18 work

Therefore, rate of work for Y should be (1/18)*(1/10) = (1/180).

1/180 work --- 1hr
1/3 work --- 180*(1/3) = 60hrs.

Thanks.

We are told that X takes 12 hours to finish a certain job, not 2/3 of the job. So:
12 hours = 1 job, not 2/3 of the job.
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21 Jan 2015, 21:41
Quote:
resh924 wrote:
Bunuel,

Can you help me with this question?

A group of 5 craftsmen, working together at the same rate, can finish a job in 3 hours. How long will it take a group of 4 apprentices working together to do the same job?
(1) Each 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.

Answer choice seems to be D.

Hi,

Could you anyone explain how we can solve the above question, using the 3 step approach identified in this thread. Although Bunuels approach is fantastic, I am unable to solve the Q using the 3 step approach as am getting confused if the work done by all 5 people in 3 hours should be 5/3 or 5*3. Kindly assist.

Thanks
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23 Mar 2015, 19:05
Can someone help me understand what is wrong with this approach for solving Example 2?

X completed 2/3 of the work which would have taken him 12 hours to complete. => X took 9 hours to complete 2/3 of the work.

Given that y takes 10 times the time, y would take 90 hours to complete 2/3rd of the work. But only 1/3rd of the work is remaianing

=> y takes 45 hours to complete the remaining work.
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05 May 2015, 17:15
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MBAhereIcome wrote:
this is a great post but, i'd suggest to use either of the below formulas depending on what the question asks.

time taken = A*B/A+B ............. where A,B is the respective time of each person/machine.
work done = W1 + W2 ............... where W1,W2 is the respective work done by each person/machine.

Can anyone help me how to use this formula for work problems?
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11 May 2015, 23:49
SivaKumarP wrote:
MBAhereIcome wrote:
this is a great post but, i'd suggest to use either of the below formulas depending on what the question asks.

time taken = A*B/A+B ............. where A,B is the respective time of each person/machine.
work done = W1 + W2 ............... where W1,W2 is the respective work done by each person/machine.

Can anyone help me how to use this formula for work problems?

Hi SivaKumarP,

The formula is an extension of the basic concept of work rate problem. Let me explain it with an example.

Assume two persons A & B working alone who complete a work $$'W'$$ in $$5$$ and $$6$$ days respectively. We need to find the time taken by A & B working together to complete the same work $$W$$.

We know the amount of work to be done (i.e. $$W$$) and are asked to find the time taken. From the work rate equation Work = Rate * Time, the only variable remaining is the rate, so let's find out the rates of persons A & B and put in the equation to calculate the time taken.

Rates of work done by A & B
Work done by A = $$W$$
Time taken by A to do W amount of work = $$5$$ days

Since Rate = Work/time

Hence rate of work done by A = $$\frac{W}{5}$$

Similarly rate of work done by B = $$\frac{W}{6}$$

Putting the values of rates of A & B in the Work Rate equation to find out the time taken when both A & B work together:

Work = Rate * Time

$$W = (\frac{W}{5} + \frac{W}{6}) * t$$ (since A & B would work for the same time 't' to complete the work when working together)

$$W = \frac{11W}{30} * t$$ i.e. $$t = \frac{30}{11}$$ days = $$\frac{(5*6)}{(5+6)}$$ days

Time taken when A & B work together to do the same work = Time taken by A * Time taken by B/(Time taken by A + Time taken by B)

On similar lines, if we need to find the work done by A & B working together for 30 days, we can calculate it using the rate of work of A & B working together which is $$\frac{11W}{30}$$.

Work done by A & B working together for 30 days = $$\frac{11W}{30} * 30 = 11W = 6W + 5W$$ i.e. work done by A & B respectively working alone for 30 days.

Work done by A & B together in time t = Work done by A in time t + Work done by B in time t

Hope its clear!

Regards
Harsh
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30 Jul 2015, 08:07
Can someone help with this question?
If it takes 4 machines, working at the same constant rate, 2 hours to complete 2 jobs, how long will it take 3 machines, working at the same constant rate, to complete 3 jobs?"

The answer is 4 hours but I have no idea how to arrive at the answer, hopefully someone can help.
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30 Jul 2015, 08:23
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JRAppz wrote:
Can someone help with this question?
If it takes 4 machines, working at the same constant rate, 2 hours to complete 2 jobs, how long will it take 3 machines, working at the same constant rate, to complete 3 jobs?"

The answer is 4 hours but I have no idea how to arrive at the answer, hopefully someone can help.

STEP BY STEP:

4 machines, 2 hours to complete 2 jobs;
1 machine, 8 hours to complete 2 jobs;
1 machine, 4 hours to complete 1 job;
3 machines, 4/3 hours to complete 1 job;
3 machines, 4 hours to complete 3 jobs.
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30 Jul 2015, 08:26
Bunuel wrote:
JRAppz wrote:
Can someone help with this question?
If it takes 4 machines, working at the same constant rate, 2 hours to complete 2 jobs, how long will it take 3 machines, working at the same constant rate, to complete 3 jobs?"

The answer is 4 hours but I have no idea how to arrive at the answer, hopefully someone can help.

STEP BY STEP:

4 machines, 2 hours to complete 2 jobs;
1 machine, 8 hours to complete 2 jobs;
1 machine, 4 hours to complete 1 job;
3 machines, 4/3 hours to complete 1 job;
3 machines, 4 hours to complete 3 jobs.

Bunuel - Could you possibly structure that in an algebraic manner?
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30 Jul 2015, 08:32
JRAppz wrote:
Bunuel wrote:
JRAppz wrote:
Can someone help with this question?
If it takes 4 machines, working at the same constant rate, 2 hours to complete 2 jobs, how long will it take 3 machines, working at the same constant rate, to complete 3 jobs?"

The answer is 4 hours but I have no idea how to arrive at the answer, hopefully someone can help.

STEP BY STEP:

4 machines, 2 hours to complete 2 jobs;
1 machine, 8 hours to complete 2 jobs;
1 machine, 4 hours to complete 1 job;
3 machines, 4/3 hours to complete 1 job;
3 machines, 4 hours to complete 3 jobs.

Bunuel - Could you possibly structure that in an algebraic manner?

Rate*Time = Job done.

(4*rate of one machine)*2 = 2;

rate of one machine = 1/4 job/hour.

Rate*Time = Job done.

(3*rate of one machine)*x = 3;

(3*1/4)*x = 3;

x = 4 hours.
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