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Re: Time n Work Problem [#permalink]
21 Nov 2013, 01:48

1

This post received KUDOS

Expert's post

AccipiterQ wrote:

Bunuel wrote:

AndreG wrote:

Hm, i got stuck cuz I got something a little different: YOURS: 3 men would do the same work 5 days sooner than 9 women --> \(\frac{m}{3}+5=\frac{w}{9}\).

MINE: 3 men would do the same work 5 days sooner than 9 women --> \(\frac{3}{m}=\frac{9}{w}+5\)

In the above equation you also have for 2 men: \(\frac{2}{m}\) - so why do u suddenly use the reciprocal? And why don't we add the 5 to women, because they take longer, hence their side is smaller...

Let one woman complete the job in \(w\) days and one man in \(m\) days.

First equation: It takes 6 days for 3 women and 2 men working together to complete a work: As the rate of 1 woman is \(\frac{1}{w}\) job/day, then the rate of 3 women will be \(\frac{3}{w}\) job/day. As the rate of 1 man is \(\frac{1}{m}\) job/day, then the rate of 2 men will be \(\frac{2}{m}\) job/day. Combined rate of 3 women and 2 men in one day will be: \(\frac{3}{w}+\frac{2}{m}\) job/day.

As they do all the job in 6 days then in 1 day they do 1/6 of the job, which is combined rate of 3 women and 2 men --> \(\frac{3}{w}+\frac{2}{m}=\frac{1}{6}\).

Second equation: 3 men would do the same work 5 days sooner than 9 women: As 1 man needs \(m\) days to do the job 3 men will need \(\frac{m}{3}\) days to do the job. As 1 woman needs \(w\) days to do the job 9 women will need \(\frac{w}{9}\) days to do the job. 3 men would do the same work 5 days sooner means that 3 men will need 5 less days to do the job, hence \(\frac{m}{3}\) is 5 less than \(\frac{w}{9}\) --> \(\frac{m}{3}+5=\frac{w}{9}\).

Hope it's clear.

My question is this, on the second equation how did you KNOW to put m/3, whereas in the first it was 2/m? In both cases aren't you figuring out the rate? In the first equation, you know that a man does 1/m of the job, and that 2 would do 2/m. In the second equation the rate is still 1/m, but you have 3 men, so should it not be 3/m+5=9/m?

Please read the solution carefully: First equation gives the rate: the rate of 1 man is \(\frac{1}{m}\) job/day, then the rate of 2 men will be \(\frac{2}{m}\) job/day.

Second equation gives time: 1 man needs \(m\) days to do the job 3 men will need \(\frac{m}{3}\) days to do the job.

Re: Time n Work Problem [#permalink]
17 Jan 2014, 22:26

Bunuel wrote:

nonameee wrote:

Guys, even if you know the solution right away, it takes several minutes (definitely more than 3) to just write it down to find the answer. Is it a real GMAT question? Can something like that be expected on the real test?

Below is another solution which is a little bit faster.

It takes 6 days for 3 women and 2 men working together to complete a work.3 men would do the same work 5 days sooner than 9 women.How many times does the output of a man exceed that of a woman? A. 3 times B. 4 times C. 5 times D. 6 times E. 7 times Let one woman complete the job in \(w\) days and one man in \(m\) days. So the rate of 1 woman is \(\frac{1}{w}\) job/day and the rate of 1 man is \(\frac{1}{m}\) job/day.

It takes 6 days for 3 women and 2 men working together to complete a work --> sum the rates: \(\frac{3}{w}+\frac{2}{m}=\frac{1}{6}\).

3 men would do the same work 5 days sooner than 9 women --> \(\frac{m}{3}+5=\frac{w}{9}\).

Solving: \(m=15\) and \(w=90\). \(\frac{w}{m}=6\).

Answer: D.

bunuel, pls help

if i equate time i am not getting it pls tell me where i am going wrong

lets take 1 woman can complete the work in 'w' days and 1 man can complete in 'm' days so, it becomes w/3+m/2=6 and m/3+5=w/9

Re: Time n Work Problem [#permalink]
18 Jan 2014, 02:22

Expert's post

saggii27 wrote:

Bunuel wrote:

nonameee wrote:

Guys, even if you know the solution right away, it takes several minutes (definitely more than 3) to just write it down to find the answer. Is it a real GMAT question? Can something like that be expected on the real test?

Below is another solution which is a little bit faster.

It takes 6 days for 3 women and 2 men working together to complete a work.3 men would do the same work 5 days sooner than 9 women.How many times does the output of a man exceed that of a woman? A. 3 times B. 4 times C. 5 times D. 6 times E. 7 times Let one woman complete the job in \(w\) days and one man in \(m\) days. So the rate of 1 woman is \(\frac{1}{w}\) job/day and the rate of 1 man is \(\frac{1}{m}\) job/day.

It takes 6 days for 3 women and 2 men working together to complete a work --> sum the rates: \(\frac{3}{w}+\frac{2}{m}=\frac{1}{6}\).

3 men would do the same work 5 days sooner than 9 women --> \(\frac{m}{3}+5=\frac{w}{9}\).

Solving: \(m=15\) and \(w=90\). \(\frac{w}{m}=6\).

Answer: D.

bunuel, pls help

if i equate time i am not getting it pls tell me where i am going wrong

lets take 1 woman can complete the work in 'w' days and 1 man can complete in 'm' days so, it becomes w/3+m/2=6 and m/3+5=w/9

but i am getting the answer wrong.

thanks in advance

That's because your equations are wrong. If one woman complete the job in \(w\) days and one man in \(m\) days, then w/3 is the time one woman needs to complete 1/3 of the work and m/2 is the time one man needs to complete 1/2 of the work. Adding them makes no sense. We can add rates but not times.

Re: Time n Work Problem [#permalink]
18 Jan 2014, 02:55

Bunuel wrote:

Guys, even if you know the solution right away, it takes several minutes (definitely more than 3) to just write it down to find the answer. Is it a real GMAT question? Can something like that be expected on the real test?

Below is another solution which is a little bit faster.

It takes 6 days for 3 women and 2 men working together to complete a work.3 men would do the same work 5 days sooner than 9 women.How many times does the output of a man exceed that of a woman? A. 3 times B. 4 times C. 5 times D. 6 times E. 7 times Let one woman complete the job in \(w\) days and one man in \(m\) days. So the rate of 1 woman is \(\frac{1}{w}\) job/day and the rate of 1 man is \(\frac{1}{m}\) job/day.

It takes 6 days for 3 women and 2 men working together to complete a work --> sum the rates: \(\frac{3}{w}+\frac{2}{m}=\frac{1}{6}\).

3 men would do the same work 5 days sooner than 9 women --> \(\frac{m}{3}+5=\frac{w}{9}\).

Solving: \(m=15\) and \(w=90\). \(\frac{w}{m}=6\).

Answer: D.[/quote]

bunuel, pls help

if i equate time i am not getting it pls tell me where i am going wrong

lets take 1 woman can complete the work in 'w' days and 1 man can complete in 'm' days so, it becomes w/3+m/2=6 and m/3+5=w/9

but i am getting the answer wrong.

thanks in advance[/quote]

That's because your equations are wrong. If one woman complete the job in \(w\) days and one man in \(m\) days, then w/3 is the time one woman needs to complete 1/3 of the work and m/2 is the time one man needs to complete 1/2 of the work. Adding them makes no sense. We can add rates but not times.

oh silly me thanks for that quick response i always get confused with the reciprocality in rates and work. is there any other way to get hold of them.?

Re: Time n Work Problem [#permalink]
18 Jan 2014, 03:03

Expert's post

saggii27 wrote:

oh silly me thanks for that quick response i always get confused with the reciprocality in rates and work. is there any other way to get hold of them.?

Re: Time n Work Problem [#permalink]
06 Feb 2014, 09:16

Bunuel wrote:

nonameee wrote:

Guys, even if you know the solution right away, it takes several minutes (definitely more than 3) to just write it down to find the answer. Is it a real GMAT question? Can something like that be expected on the real test?

Below is another solution which is a little bit faster.

It takes 6 days for 3 women and 2 men working together to complete a work.3 men would do the same work 5 days sooner than 9 women.How many times does the output of a man exceed that of a woman? A. 3 times B. 4 times C. 5 times D. 6 times E. 7 times

Let one woman complete the job in \(w\) days and one man in \(m\) days. So the rate of 1 woman is \(\frac{1}{w}\) job/day and the rate of 1 man is \(\frac{1}{m}\) job/day.

It takes 6 days for 3 women and 2 men working together to complete a work --> sum the rates: \(\frac{3}{w}+\frac{2}{m}=\frac{1}{6}\).

3 men would do the same work 5 days sooner than 9 women --> \(\frac{m}{3}+5=\frac{w}{9}\).

Solving: \(m=15\) and \(w=90\). \(\frac{w}{m}=6\).

Answer: D.

I stumbled on this answer and think it's worth clarifying:

In the second equation: 3 men would do the same work 5 days sooner than 9 women --> \(\frac{m}{3}+5=\frac{w}{9}\).

m and w are representing TOTAL work done by men and women.

Whereas in the first equation: Let one woman complete the job in \(w\) days and one man in \(m\) days. So the rate of 1 woman is \(\frac{1}{w}\) job/day and the rate of 1 man is \(\frac{1}{m}\) job/day.

m and w are representing the RATE of work done by men and women.

I hope this is correct (Bunuel can you confirm?) and has helped some grasp the concept.

Re: Time n Work Problem [#permalink]
07 Feb 2014, 03:57

Expert's post

mrwells2 wrote:

Bunuel wrote:

nonameee wrote:

Guys, even if you know the solution right away, it takes several minutes (definitely more than 3) to just write it down to find the answer. Is it a real GMAT question? Can something like that be expected on the real test?

Below is another solution which is a little bit faster.

It takes 6 days for 3 women and 2 men working together to complete a work.3 men would do the same work 5 days sooner than 9 women.How many times does the output of a man exceed that of a woman? A. 3 times B. 4 times C. 5 times D. 6 times E. 7 times

Let one woman complete the job in \(w\) days and one man in \(m\) days. So the rate of 1 woman is \(\frac{1}{w}\) job/day and the rate of 1 man is \(\frac{1}{m}\) job/day.

It takes 6 days for 3 women and 2 men working together to complete a work --> sum the rates: \(\frac{3}{w}+\frac{2}{m}=\frac{1}{6}\).

3 men would do the same work 5 days sooner than 9 women --> \(\frac{m}{3}+5=\frac{w}{9}\).

Solving: \(m=15\) and \(w=90\). \(\frac{w}{m}=6\).

Answer: D.

I stumbled on this answer and think it's worth clarifying:

In the second equation: 3 men would do the same work 5 days sooner than 9 women --> \(\frac{m}{3}+5=\frac{w}{9}\).

m and w are representing TOTAL work done by men and women.

Whereas in the first equation: Let one woman complete the job in \(w\) days and one man in \(m\) days. So the rate of 1 woman is \(\frac{1}{w}\) job/day and the rate of 1 man is \(\frac{1}{m}\) job/day.

m and w are representing the RATE of work done by men and women.

I hope this is correct (Bunuel can you confirm?) and has helped some grasp the concept.

No, that's not correct.

m and w in both equations represent the same thing: time.

w is the number of days (time) one woman needs complete the job. m is the number of days (time) one man needs complete the job.

Re: It takes 6 days for 3 women and 2 men working together to [#permalink]
16 Apr 2014, 00:51

one man can complete the work in m days. (1/m)th of the work will completed per day.

women completes the work in n days. (1/n)th of the work will be completed per day. Their combined rate/day = 1/m + 1/n;

(1/m)th of the work will completed per day by one man. ??? ----------------------- by 3 man (2/m)th of the work will be completed by 2 men /day (1/n)th of the work will be completed per day by one woman/day. ??? --------------------------- by 3 women (3/n)th of work will be completed by 3 women/day. It takes 6 days for 3 women and 2 men working together to complete a work. So, (1/6)th of the work will be completed by 3 women and 2 men working together per day. 2/m + 3/n = 1/6;

3 men would do the same work 5 days sooner than 9 women. 1 man needs m days to do the job 3 men will need m/3 days to do the job. As 1 woman needs n days to do the job 9 women will need n/9 days to do the same job.

3 men would do the same work 5 days sooner than 9 women. m/3 +5 =n/9

Re: It takes 6 days for 3 women and 2 men working together to [#permalink]
03 Sep 2014, 12:56

Hi Guys. Is there a way to do this without much time? Some way to get to a good point to guess? I saw IanStewart's post, but was wondering if someone has another idea?

It takes 6 days for 3 women and 2 men working together to [#permalink]
17 Oct 2014, 20:50

Bunuel wrote:

nonameee wrote:

Guys, even if you know the solution right away, it takes several minutes (definitely more than 3) to just write it down to find the answer. Is it a real GMAT question? Can something like that be expected on the real test?

Below is another solution which is a little bit faster.

It takes 6 days for 3 women and 2 men working together to complete a work.3 men would do the same work 5 days sooner than 9 women.How many times does the output of a man exceed that of a woman? A. 3 times B. 4 times C. 5 times D. 6 times E. 7 times

Let one woman complete the job in \(w\) days and one man in \(m\) days. So the rate of 1 woman is \(\frac{1}{w}\) job/day and the rate of 1 man is \(\frac{1}{m}\) job/day.

It takes 6 days for 3 women and 2 men working together to complete a work --> sum the rates: \(\frac{3}{w}+\frac{2}{m}=\frac{1}{6}\).

3 men would do the same work 5 days sooner than 9 women --> \(\frac{m}{3}+5=\frac{w}{9}\).

Solving: \(m=15\) and \(w=90\). \(\frac{w}{m}=6\).

Answer: D.

This is where i got my answer wrong: my equation is 3/m -9/w = 1/5

Re: It takes 6 days for 3 women and 2 men working together to [#permalink]
21 Oct 2014, 14:03

It takes 6 days for 3 women and 2 men working together to complete a work.3 men would do the same work 5 days sooner than 9 women.How many times does the output of a man exceed that of a woman? A. 3 times B. 4 times C. 5 times D. 6 times E. 7 times

Let one woman complete the job in w days and one man in m days. So the rate of 1 woman is \frac{1}{w} job/day and the rate of 1 man is \frac{1}{m} job/day.

It takes 6 days for 3 women and 2 men working together to complete a work --> sum the rates: \frac{3}{w}+\frac{2}{m}=\frac{1}{6}.

3 men would do the same work 5 days sooner than 9 women --> \frac{m}{3}+5=\frac{w}{9}.

Solving: m=15 and w=90. \frac{w}{m}=6.

Answer: D.

Bunnel, If men work 5 days less than women why are we adding 5 in equation 3/w? Dont we should minus 5 days ( t-5).

Re: It takes 6 days for 3 women and 2 men working together to [#permalink]
21 Oct 2014, 14:06

1

This post was BOOKMARKED

Hi Bunnel,

I am a bit confuse here if men have taken 5 days less than whya re we adding 5 days, shouldn't we need to subtract 5 days. Women time/day = d Men time/day = d-5

Re: It takes 6 days for 3 women and 2 men working together to [#permalink]
22 Oct 2014, 00:17

Expert's post

taleesh wrote:

It takes 6 days for 3 women and 2 men working together to complete a work.3 men would do the same work 5 days sooner than 9 women.How many times does the output of a man exceed that of a woman? A. 3 times B. 4 times C. 5 times D. 6 times E. 7 times

Let one woman complete the job in w days and one man in m days. So the rate of 1 woman is \frac{1}{w} job/day and the rate of 1 man is \frac{1}{m} job/day.

It takes 6 days for 3 women and 2 men working together to complete a work --> sum the rates: \frac{3}{w}+\frac{2}{m}=\frac{1}{6}.

3 men would do the same work 5 days sooner than 9 women --> \frac{m}{3}+5=\frac{w}{9}.

Solving: m=15 and w=90. \frac{w}{m}=6.

Answer: D.

Bunnel, If men work 5 days less than women why are we adding 5 in equation 3/w? Dont we should minus 5 days ( t-5).

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