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Re: Time n Work Problem [#permalink]

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New post 15 Sep 2012, 11:06
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 \(3^3.\)
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Re: It takes 6 days for 3 women and 2 men working together to [#permalink]

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New post 15 Sep 2012, 11:53
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.

Answer D.
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Re: Time n Work Problem [#permalink]

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New post 19 Sep 2012, 15:56
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 \(w=90\). \(\frac{w}{m}=6\).

Answer: D.



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.

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Re: Time n Work Problem [#permalink]

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New post 19 Sep 2012, 23:39
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 \(w=90\). \(\frac{w}{m}=6\).

Answer: D.



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
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Re: Time n Work Problem [#permalink]

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New post 18 Feb 2013, 16:57
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.

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

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New post 19 Feb 2013, 03:13
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.
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Last edited by mau5 on 05 Jul 2013, 02:28, edited 1 time in total.

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Re: Time n Work Problem [#permalink]

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New post 21 Feb 2013, 07:11
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.

Can anybody please help??

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Re: Time n Work Problem [#permalink]

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New post 30 Sep 2013, 01:44
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 \(w=90\). \(\frac{w}{m}=6\).

Answer: D.



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 --> \(\frac{m}{3}+5=\frac{w}{9}\).
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Re: Time n Work Problem [#permalink]

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New post 30 Sep 2013, 02:07
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 \(w=90\). \(\frac{w}{m}=6\).

Answer: D.



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.
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Re: Time n Work Problem [#permalink]

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New post 17 Oct 2013, 10:25
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 \(w=90\). \(\frac{w}{m}=6\).


Answer: D.


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...

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Re: Time n Work Problem [#permalink]

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New post 17 Oct 2013, 10:37
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 \(w=90\). \(\frac{w}{m}=6\).


Answer: D.


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...


Please check here: it-takes-6-days-for-3-women-and-2-men-working-together-to-82718-20.html#p1272526
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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

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Re: Time n Work Problem [#permalink]

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New post 17 Oct 2013, 10:50
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.


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?

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Re: Time n Work Problem [#permalink]

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New post 17 Oct 2013, 10:56
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 \(w=90\). \(\frac{w}{m}=6\).

Answer: D.


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).
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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

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Re: Time n Work Problem [#permalink]

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New post 17 Oct 2013, 11:08
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 \(w=90\). \(\frac{w}{m}=6\).

Answer: D.



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.

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Re: Time n Work Problem [#permalink]

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New post 17 Oct 2013, 11:12
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 \(w=90\). \(\frac{w}{m}=6\).

Answer: D.



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
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Re: Time n Work Problem [#permalink]

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New post 17 Oct 2013, 11:15
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 \(w=90\). \(\frac{w}{m}=6\).

Answer: D.



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?

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

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New post 26 Oct 2013, 11:08
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.

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Re: Time n Work Problem [#permalink]

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New post 20 Nov 2013, 11:58
Bunuel wrote:
AndreG 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 \(w=90\). \(\frac{w}{m}=6\).

Answer: D.


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?

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Re: Time n Work Problem [#permalink]

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New post 31 Dec 2013, 15:11
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, 06:54, edited 1 time in total.

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Re: Time n Work Problem   [#permalink] 31 Dec 2013, 15:11

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