Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 06 Oct 2015, 20:25

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:
Director
Joined: 22 Mar 2011
Posts: 612
WE: Science (Education)
Followers: 80

Kudos [?]: 667 [0], given: 43

Re: Time n Work Problem [#permalink]  15 Sep 2012, 10:06
Bunuel wrote:
sam2010 wrote:
Bunel-I got a quadratic equation while solving these two eqn. Is there a simple way of solving them?

I also got quadratic equation ($$m^2-3m-180=0$$) and it wasn't too hard to solve (discriminant would be perfect square $$d=3^3+4*180=729=27^2$$) --> $$m=-12$$ or $$m=15$$.

Just a smal typo: in the discriminant, it should be $$3^2$$ and not $$3^3.$$
_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Director
Joined: 22 Mar 2011
Posts: 612
WE: Science (Education)
Followers: 80

Kudos [?]: 667 [0], given: 43

Re: It takes 6 days for 3 women and 2 men working together to [#permalink]  15 Sep 2012, 10:53
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

The fastest and easiest way to solve this question was already proposed by IanStewart.

I am trying another algebraic approach.

Denote by $$W$$ the rate of a woman, by $$M$$ that of a men, and by $$T$$ the time it takes 9 women to complete the work.
We have the following equations:
$$6(3W + 2M) = 9WT = 3M(T-5)$$, or, after reducing by 3, $$2(3W + 2M) = 3WT = M(T - 5).$$
We are looking for the ratio $$M/W$$ which we can denote by $$n.$$ Substituting in the above equations $$M = nW,$$ we can write:
$$2(3W + 2nW) = 3WT = nW(T - 5).$$

Divide through by $$W,$$ so $$6 + 4n = 3T = nT - 5n.$$ Solving for $$T$$ (equality between the last two expressions) we obtain $$T=\frac{5n}{n-3}.$$
Taking the equality of the first two expressions, we get $$6+4n=\frac{3\cdot{5}n}{n-3}.$$
From the possible answer choices we can deduce that $$n$$ must be a positive integer.
We need $$\frac{15n}{n-3}$$ to be a positive integer. We can see that $$n$$ cannot be odd and it must be greater than 3.
We have to choose between B and D.
Only $$n = 6$$ works.

_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Senior Manager
Joined: 24 Mar 2010
Posts: 347
Followers: 7

Kudos [?]: 80 [0], given: 4

Re: Time n Work Problem [#permalink]  19 Sep 2012, 14:56
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 $$w=90$$. $$\frac{w}{m}=6$$.

How did you solve for m and w in the very last part? I do the algebra and can't get the right answer. You have one equation with 2 unknown variables.
Director
Joined: 22 Mar 2011
Posts: 612
WE: Science (Education)
Followers: 80

Kudos [?]: 667 [0], given: 43

Re: Time n Work Problem [#permalink]  19 Sep 2012, 22:39
Shawshank 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 $$w=90$$. $$\frac{w}{m}=6$$.

How did you solve for m and w in the very last part? I do the algebra and can't get the right answer. You have one equation with 2 unknown variables.

You have 2 equations with two unknowns:
First equation $$\frac{3}{w}+\frac{2}{m}=\frac{1}{6}.$$
Second equation $$\frac{m}{3}+5=\frac{w}{9}$$.
After getting rid of the denominators (multiply first equation by $$6wm$$ and the second by 9), for example express $$w$$
from the second equation and substitute it into the first. You obtain a quadratic equation for $$m$$:

$$m^2-3m-180=0$$

This equation has one positive and one negative root. The sum of the two roots must be 3 and their product -180.
Using factorization for 180, you can find -12 and 15.
So $$m=15$$ and $$w=90.$$

For another algebraic approach see:
it-takes-6-days-for-3-women-and-2-men-working-together-to-82718.html#p1121807
_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Manager
Joined: 08 Dec 2012
Posts: 67
Location: United Kingdom
GMAT 1: 710 Q0 V0
WE: Engineering (Consulting)
Followers: 1

Kudos [?]: 97 [0], given: 31

Re: It takes 6 days for 3 women and 2 men working together to [#permalink]  18 Feb 2013, 13:51
Struggling to finish this in 3 minutes, did anyone manage to completely solve it within 3 mins?
Manager
Joined: 24 Jan 2013
Posts: 81
Followers: 5

Kudos [?]: 105 [0], given: 6

Re: Time n Work Problem [#permalink]  18 Feb 2013, 15:57
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?

Completely agree... I did GMAT two years ago and by far the questions were not that complicated. Complicated, of course. But not that complicated. As you can see on my blog, studying GMAT is basically using the Official book and maybe one or two other books for reinforcement. Look for my advice. There is not "rocket science".

I also say GMAT preparation should not mean spending more than \$100.
_________________

Does this post deserve KUDOS?

Free Flashcards: Free GMAT Flashcards

There are many things you want to know before doing the GMAT exam (how is exam day, what to expect, how to think, to do's...), and you have them in this blog, in a simple way

Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 629
Followers: 65

Kudos [?]: 798 [0], given: 135

Re: It takes 6 days for 3 women and 2 men working together to [#permalink]  19 Feb 2013, 02:13
Expert's post
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

Maybe a method only suitable for GMAT :

We know that Work = rate*time.

Let m = rate of work of each man in one day and so on for w(each women)

As the work done is the same for 3 men/9 women;

$$3*m*t = 9*w*(t+5)$$

or $$\frac{m}{w} = 3\frac{(t+5)}{t}$$ = $$3*(1+\frac{5}{t})$$ = $$3+3*\frac{5}{t}$$

Now we go back to the options, and see that each of them is an integer. Thus, m/w, which is required can only be an integer and also a multiple of 3. The only multiple present can be 6, for t=5.

D.
_________________

Last edited by mau5 on 05 Jul 2013, 01:28, edited 1 time in total.
Intern
Joined: 21 Feb 2013
Posts: 13
Followers: 0

Kudos [?]: 1 [0], given: 0

Re: Time n Work Problem [#permalink]  21 Feb 2013, 06:11
Bunuel wrote:
sam2010 wrote:
Bunel-I got a quadratic equation while solving these two eqn. Is there a simple way of solving them?

I also got quadratic equation ($$m^2-3m-180=0$$) and it wasn't too hard to solve (discriminant would be perfect square $$d=3^3+4*180=729=27^2$$) --> $$m=-12$$ or $$m=15$$.

My friend, I'm ending up with 12w+18m=mw and 9m+135=3w

2/m+3/w=1/6

take lcm and you end up with 12w+18m=mw

same with m/3+5=w/9, I end up with 9m+135=3w

With that I get some very large numbers when trying to solve so I'm pretty sure I'm not doing it right.

Math Expert
Joined: 02 Sep 2009
Posts: 29750
Followers: 4895

Kudos [?]: 53391 [0], given: 8155

Re: It takes 6 days for 3 women and 2 men working together to [#permalink]  05 Jul 2013, 01:27
Expert's post
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

_________________
Director
Joined: 17 Apr 2013
Posts: 636
Schools: HBS '16
GMAT 1: 710 Q50 V36
GMAT 2: 750 Q51 V41
GMAT 3: 790 Q51 V49
GPA: 3.3
Followers: 22

Kudos [?]: 172 [0], given: 284

Re: Time n Work Problem [#permalink]  30 Sep 2013, 00:44
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 $$w=90$$. $$\frac{w}{m}=6$$.

Can you please help me to understand on what logic did you make this explanation- 3 men would do the same work 5 days sooner than 9 women --> $$\frac{m}{3}+5=\frac{w}{9}$$.
_________________

Like my post Send me a Kudos It is a Good manner.
My Debrief: how-to-score-750-and-750-i-moved-from-710-to-189016.html

Math Expert
Joined: 02 Sep 2009
Posts: 29750
Followers: 4895

Kudos [?]: 53391 [0], given: 8155

Re: Time n Work Problem [#permalink]  30 Sep 2013, 01:07
Expert's post
honchos 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 $$w=90$$. $$\frac{w}{m}=6$$.

Can you please help me to understand on what logic did you make this explanation- 3 men would do the same work 5 days sooner than 9 women --> $$\frac{m}{3}+5=\frac{w}{9}$$.

One man completes the job in $$m$$ days --> 3 men in m/3 days.
One woman completes the job in $$w$$ days --> 9 women in w/9 days.

We are told that m/3 is 5 less than w/9 --> $$\frac{m}{3}+5=\frac{w}{9}$$.

Hope it's clear.
_________________
Director
Joined: 17 Apr 2013
Posts: 636
Schools: HBS '16
GMAT 1: 710 Q50 V36
GMAT 2: 750 Q51 V41
GMAT 3: 790 Q51 V49
GPA: 3.3
Followers: 22

Kudos [?]: 172 [0], given: 284

Re: Time n Work Problem [#permalink]  30 Sep 2013, 01:11
Yes thanks, it was an ab initio approach, I thought some formula. Thanks a Lot.
_________________

Like my post Send me a Kudos It is a Good manner.
My Debrief: how-to-score-750-and-750-i-moved-from-710-to-189016.html

Current Student
Joined: 26 Sep 2013
Posts: 229
Concentration: Finance, Economics
GMAT 1: 670 Q39 V41
GMAT 2: 730 Q49 V41
Followers: 2

Kudos [?]: 76 [0], given: 40

Re: Time n Work Problem [#permalink]  17 Oct 2013, 09:25
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'm just not having a good day here haha.... if the rate for 3 men to do the same work 5 days sooner than 9 woman, shouldn't the equation be $$\frac{3}{m}+5=\frac{9}{w}$$? Since the rate of 1 woman is 1/w, and for one man is 1/m. If you have 3 men, then you have 3/m, and if you have 9 women you have 9/w...
Math Expert
Joined: 02 Sep 2009
Posts: 29750
Followers: 4895

Kudos [?]: 53391 [0], given: 8155

Re: Time n Work Problem [#permalink]  17 Oct 2013, 09:37
Expert's post
AccipiterQ 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'm just not having a good day here haha.... if the rate for 3 men to do the same work 5 days sooner than 9 woman, shouldn't the equation be $$\frac{3}{m}+5=\frac{9}{w}$$? Since the rate of 1 woman is 1/w, and for one man is 1/m. If you have 3 men, then you have 3/m, and if you have 9 women you have 9/w...

_________________
Current Student
Joined: 26 Sep 2013
Posts: 229
Concentration: Finance, Economics
GMAT 1: 670 Q39 V41
GMAT 2: 730 Q49 V41
Followers: 2

Kudos [?]: 76 [0], given: 40

Re: Time n Work Problem [#permalink]  17 Oct 2013, 09:50
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 $$w=90$$. $$\frac{w}{m}=6$$.

Thanks for previous reply. I'm getting stuck at this point though...so the party I've highlighted in green, is that even necessary to solve? The part in red seems to be the key, and then did you just keep plugging numbers in until you got the solution for the blue? I see you said "solving:" before that line, but there's no computations, is it just fairly simple plugging in of numbers?
Math Expert
Joined: 02 Sep 2009
Posts: 29750
Followers: 4895

Kudos [?]: 53391 [0], given: 8155

Re: Time n Work Problem [#permalink]  17 Oct 2013, 09:56
Expert's post
AccipiterQ 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 $$w=90$$. $$\frac{w}{m}=6$$.

Thanks for previous reply. I'm getting stuck at this point though...so the party I've highlighted in green, is that even necessary to solve? The part in red seems to be the key, and then did you just keep plugging numbers in until you got the solution for the blue? I see you said "solving:" before that line, but there's no computations, is it just fairly simple plugging in of numbers?

You need to solve. Check here: it-takes-6-days-for-3-women-and-2-men-working-together-to-82718-20.html#p1123335 (Please read a topic entirely, this might help in many cases).
_________________
Current Student
Joined: 26 Sep 2013
Posts: 229
Concentration: Finance, Economics
GMAT 1: 670 Q39 V41
GMAT 2: 730 Q49 V41
Followers: 2

Kudos [?]: 76 [0], given: 40

Re: Time n Work Problem [#permalink]  17 Oct 2013, 10:08
Bunuel wrote:
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 think the part I'm getting confused by is this:

Bunuel wrote:
So the rate of 1 woman is $$\frac{1}{w}$$ job/day and the rate of 1 man is $$\frac{1}{m}$$ job/day.

I get that part.

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

I get this part as well, because 3*$$\frac{1}{w}$$= $$\frac{3}{w}$$, and the same for the men's rate. But here's where I get lost:

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

Using the logic from the second quote, 3 men doing the same work 5 days sooner than 9 women would be 3*$$\frac{1}{m}$$+5 = 9*$$\frac{1}{w}$$. I don't understand how we can just switch whether the multiplier goes in the numerator or the denominator like that. Because their work rates are remaining the same; 1 man will do 1/m no matter what, so 3 men should always do 3/m, not m/3.
Math Expert
Joined: 02 Sep 2009
Posts: 29750
Followers: 4895

Kudos [?]: 53391 [0], given: 8155

Re: Time n Work Problem [#permalink]  17 Oct 2013, 10:12
Expert's post
AccipiterQ wrote:
Bunuel wrote:
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 think the part I'm getting confused by is this:

Bunuel wrote:
So the rate of 1 woman is $$\frac{1}{w}$$ job/day and the rate of 1 man is $$\frac{1}{m}$$ job/day.

I get that part.

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

I get this part as well, because 3*$$\frac{1}{w}$$= $$\frac{3}{w}$$, and the same for the men's rate. But here's where I get lost:

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

Using the logic from the second quote, 3 men doing the same work 5 days sooner than 9 women would be 3*$$\frac{1}{m}$$+5 = 9*$$\frac{1}{w}$$. I don't understand how we can just switch whether the multiplier goes in the numerator or the denominator like that. Because their work rates are remaining the same; 1 man will do 1/m no matter what, so 3 men should always do 3/m, not m/3.

That part is explained here: it-takes-6-days-for-3-women-and-2-men-working-together-to-82718-20.html#p1272526
_________________
Current Student
Joined: 26 Sep 2013
Posts: 229
Concentration: Finance, Economics
GMAT 1: 670 Q39 V41
GMAT 2: 730 Q49 V41
Followers: 2

Kudos [?]: 76 [0], given: 40

Re: Time n Work Problem [#permalink]  17 Oct 2013, 10:15
Bunuel wrote:
AccipiterQ wrote:
Bunuel wrote:
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 think the part I'm getting confused by is this:

Bunuel wrote:
So the rate of 1 woman is $$\frac{1}{w}$$ job/day and the rate of 1 man is $$\frac{1}{m}$$ job/day.

I get that part.

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

I get this part as well, because 3*$$\frac{1}{w}$$= $$\frac{3}{w}$$, and the same for the men's rate. But here's where I get lost:

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

Using the logic from the second quote, 3 men doing the same work 5 days sooner than 9 women would be 3*$$\frac{1}{m}$$+5 = 9*$$\frac{1}{w}$$. I don't understand how we can just switch whether the multiplier goes in the numerator or the denominator like that. Because their work rates are remaining the same; 1 man will do 1/m no matter what, so 3 men should always do 3/m, not m/3.

That part is explained here: it-takes-6-days-for-3-women-and-2-men-working-together-to-82718-20.html#p1272526

ooooh wait, I get it now, if you have 3 men working at rate m, then it will take 1/3 as long to complete their portion as a single man would do. Whereas in the other quote, you're just using the rate of 1/m, and then not adjusting the rate, just stating that 2 of them working at that rate will complete a job in 2/m, and in the green quote, we have the actual number of days it takes given, whereas in the last quote we only have each gender's rate for comparison. Yes?
Senior Manager
Joined: 10 Mar 2013
Posts: 264
Followers: 1

Kudos [?]: 39 [0], given: 2211

Re: It takes 6 days for 3 women and 2 men working together to [#permalink]  26 Oct 2013, 10:08
This looks like a crazy question.
I got
3/w + 2/m = 1/6 and m/3 = w/9 - 5 and I can't solve both of these two equations under 2 minutes.
Re: It takes 6 days for 3 women and 2 men working together to   [#permalink] 26 Oct 2013, 10:08

Go to page   Previous    1   2   3    Next  [ 56 posts ]

Similar topics Replies Last post
Similar
Topics:
1 The ratio of men to women at a banquet is 6:5. If ten men leave the pa 1 12 Sep 2015, 11:48
8 If 6 men can do a piece of work in 30 days of 9 hours each, 6 15 Jan 2014, 22:50
2 3 men and 3 women need to be seated in 2 rows with 3 chairs 5 28 Sep 2010, 05:47
6 A work crew of 4 Men takes 5 days to complete one-half of a 10 13 Mar 2010, 08:24
14 It takes 6 days for 3 women and 2 men working together to 13 12 Mar 2010, 22:33
Display posts from previous: Sort by