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# It takes 6 days for 3 women and 2 men working together to

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Re: Time n Work Problem [#permalink]

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21 Nov 2013, 01:48
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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?

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.

Hope it's clear.
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Re: Time n Work Problem [#permalink]

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31 Dec 2013, 14:11
OK I think I think I found an easy algebraic solution to solve this one.

Let's begin with the second equation

W/9 - M/3 = 5

We have from here that w = 3m + 45
So we have that w = 3(m+15)

Now replace in the first equation 3/3(m+15) + 2/m = 1/6

The 3's cancel out and we are left with 1/(m+15)+2/m=1/6

We finally are left with a quadratic equation namely m^2 - 2m - 180. From here we have that m = 15

Replacing back in w= 3 (m+15) we have that w = 90.

So w/m = 90/15 = 6

Hope this helps
Cheers
J

Last edited by jlgdr on 19 Feb 2014, 05:54, edited 1 time in total.
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Re: Time n Work Problem [#permalink]

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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 $$w=90$$. $$\frac{w}{m}=6$$.

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.

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Re: Time n Work Problem [#permalink]

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18 Jan 2014, 02:22
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 $$w=90$$. $$\frac{w}{m}=6$$.

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.

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.

Check here: it-takes-6-days-for-3-women-and-2-men-working-together-to-82718.html#p751436

Hope this helps.
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Re: Time n Work Problem [#permalink]

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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 $$w=90$$. $$\frac{w}{m}=6$$.

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.

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.

Check here: it-takes-6-days-for-3-women-and-2-men-working-together-to-82718.html#p751436

Hope this helps.[/quote]

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.?
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Re: Time n Work Problem [#permalink]

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18 Jan 2014, 03:03
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.?

Please check the following post: new-project-review-discuss-and-get-kudos-points-153555.html#p1230606

Hope it helps.
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Re: Time n Work Problem [#permalink]

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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 $$w=90$$. $$\frac{w}{m}=6$$.

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.
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Re: Time n Work Problem [#permalink]

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07 Feb 2014, 03:57
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 $$w=90$$. $$\frac{w}{m}=6$$.

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.

The following posts might help:
it-takes-6-days-for-3-women-and-2-men-working-together-to-82718.html#p751436
it-takes-6-days-for-3-women-and-2-men-working-together-to-82718-20.html#p1272526
it-takes-6-days-for-3-women-and-2-men-working-together-to-82718-40.html#p1295389
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Re: It takes 6 days for 3 women and 2 men working together to [#permalink]

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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

m/n =6;
Hence D;
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Re: It takes 6 days for 3 women and 2 men working together to [#permalink]

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02 Sep 2014, 05:38
say if we express the first eqn in days then will the below eqn is fine . please correct me.

w/3 +m/2 = 6.
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Re: It takes 6 days for 3 women and 2 men working together to [#permalink]

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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?
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It takes 6 days for 3 women and 2 men working together to [#permalink]

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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 $$w=90$$. $$\frac{w}{m}=6$$.

This is where i got my answer wrong: my equation is 3/m -9/w = 1/5
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Re: It takes 6 days for 3 women and 2 men working together to [#permalink]

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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.

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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Re: It takes 6 days for 3 women and 2 men working together to [#permalink]

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

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22 Oct 2014, 00:17
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.

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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Re: It takes 6 days for 3 women and 2 men working together to [#permalink]

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12 Aug 2015, 06:01
virtualanimosity 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

2m and 3w can do a work in 6 days or 12m and 18w in 1 day
let 9 w take x days, then 3 m will take x-5 days
that implies 1 w can complete 1/9x work in 1 day and 1 m can complete 1/(3x-15) work in 1 day
therefore, 12/(3x-15) + 18/9x = 1
solving we get x = 1 or 10
x does not take the value 1
so, 1m can do the work in 15 days and 1 w does the same work in 90 days.
Re: It takes 6 days for 3 women and 2 men working together to   [#permalink] 12 Aug 2015, 06:01

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