Question 1039507
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If the job is done in 5 days at 7 hours per day, then the whole job is done in 35 hours.  Hence, *[tex \Large \frac{1}{35}] of the job is done in one hour by 2 men and 3 women. So if *[tex \Large x] represents the fraction of the job done by one man in one hour, and *[tex \Large y] represents the fraction of the job done by one woman in one hour, we can say:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2x\ +\ 3y\ =\ \frac{1}{35}]


Using similar analysis:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 4x\ +\ 4y\ =\ \frac{1}{21}]


First, solve the 2X2 system.  I recommend the elimination method.  Multiply the first equation by -20 and the second by 15:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ -40x\ -\ 60y\ =\ -\frac{4}{7}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 60x\ +\ 60y\ =\ \frac{5}{7}]


Then add



*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 20x\ =\ \frac{1}{7}]



*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ \frac{1}{140}]


Since we want to know about a scenario where only men are working on the job we don't need to solve for *[tex \Large y].


Since one man does *[tex \Large \frac{1}{140}] of the job in one hour, 7 men do *[tex \Large \frac{1}{20}] of the job in one hour.  Therefore they need to work 20 hours to get the whole job done.  If they work 4 hours per day, then it will take 5 days.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
<img src="http://c0rk.blogs.com/gr0undzer0/darwin-fish.jpg">
*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \  

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