SOLUTION: 4 men and 3 women do work for six days 5 men and 6 women do the some job for four days. how long will it take for one woman to do the same work

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Question 930425: 4 men and 3 women do work for six days 5 men and 6 women do the some job for four days. how long will it take for one woman to do the same work
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
4 men and 3 women do work for six days 5 men and 6 women do the some job for four days. how long will it take for one woman to do the same work.
Suppose it takes one man x days to do the job.

Then his work rate is 1 job per x days or matrix%281%2C2%2C1%2Cjob%29%2Fmatrix%281%2C2%2Cx%2Cdays%29 or matrix%281%2C2%2C1%2Fx%2Cjob%2Fday%29


Suppose it takes one woman y days to do the job.

Then her work rate is 1 job per y days or matrix%281%2C2%2C1%2Cjob%29%2Fmatrix%281%2C2%2Cy%2Cdays%29 or matrix%281%2C2%2C1%2Fy%2Cjob%2Fday%29

4 men's and 3 women's combined work rate is 1 job per 6 days or matrix%281%2C2%2C1%2Cjob%29%2Fmatrix%281%2C2%2C6%2Cdays%29 or 
matrix%281%2C2%2C1%2F6%2Cjob%2Fday%29 

Therefore the first equation comes from:

%28matrix%284%2C1%2C%0D%0A%0D%0A4%2C%22men%27s%22%2C+work%2Crate%29%29%22%22%2B%22%22%28matrix%284%2C1%2C%0D%0A%0D%0A3%2C%22women%27s%22%2C+work%2Crate%29%29%22%22=%22%22%28matrix%284%2C1%2C%0D%0A%0D%0ATheir%2Ccombined%2C+work%2Crate%29%29

4%2Fx%22%22%2B%22%223%2Fy%22%22=%22%221%2F6

5 men and 6 women do the some job for four days.
5 men's and 6 women's combined work rate is 1 job per 4 days or matrix%281%2C2%2C1%2Cjob%29%2Fmatrix%281%2C2%2C4%2Cdays%29 or 
matrix%281%2C2%2C1%2F4%2Cjob%2Fday%29 

---

Therefore the second equation comes from:

%28matrix%284%2C1%2C%0D%0A%0D%0A5%2C%22men%27s%22%2C+work%2Crate%29%29%22%22%2B%22%22%28matrix%284%2C1%2C%0D%0A%0D%0A6%2C%22women%27s%22%2C+work%2Crate%29%29%22%22=%22%22%28matrix%284%2C1%2C%0D%0A%0D%0ATheir%2Ccombined%2C+work%2Crate%29%29

5%2Fx%22%22%2B%22%226%2Fy%22%22=%22%221%2F4

So we solve the resulting system of equations:

system%284%2Fx%2B3%2Fy=1%2F6%2C5%2Fx%2B6%2Fy=1%2F4%29

When solving, DO NOT clear of fractions!

Multiply first equation by -2 to cause %2B3%2Fy%29%29%29%0D%0Ato+become+%7B%7B%7B-6%2Fy to cancel out the y'terms:

system%28-8%2Fx-6%2Fy=-1%2F3%2C5%2Fx%2B6%2Fy=1%2F4%29

Adding the two equations gives:

-3%2Fx=-1%2F3%2B1%2F4

Now it's OK to clear of fractions

-36=-4x%2B3x
-36=-x
x=36

Substitute 36 for x in

4%2Fx%2B3%2Fy=1%2F6
4%2F36%2B3%2Fy=1%2F6
1%2F9%2B3%2Fy=1%2F6
Clear of fractions:
2y%2B54=3y
54=y

So it takes a man 36 days and a woman 54 days to do the job.

Edwin