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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] New post 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?


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.

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

D is the correct answer

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] New post 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

but i am getting the answer wrong.

thanks in advance
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Re: Time n Work Problem [#permalink] New post 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.

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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RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Time n Work Problem [#permalink] New post 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.

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] New post 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.?


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

Hope it helps.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Time n Work Problem [#permalink] New post 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.
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Re: Time n Work Problem [#permalink] New post 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.

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
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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