SOLUTION: six men or eight women can do a work in 15 days.How many men should work along with four women to complete the work in 10 days? A)6 B)5

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Question 824881: six men or eight women can do a work in 15 days.How many men should work along with four women to complete the work in 10 days?
A)6
B)5
Answer by Edwin McCravy(20065) About Me  (Show Source):
You can put this solution on YOUR website!
six men or eight women can do a work in 15 days.
Six men's work rate is 1 work per 15 days or 1_work%29%2F%2815_days%29 or 1%2F15%28work%29%2F%28day%29

So one men's work rate is 1%2F6 of 1%2F15%28work%29%2F%28day%29 or 1%2F90%28work%29%2F%28day%29

Eight women's work rate is also 1 work per 15 days or 1_work%29%2F%2815_days%29 or 1%2F15%28work%29%2F%28day%29

So one woman's work rate is 1%2F8 of 1%2F15%28work%29%2F%28day%29 or 1%2F120%28work%29%2F%28day%29
How many men should work along with four women to complete the work in 10 days?
Let the answer be x men.

Their combined work rate must equal 1 work per 10 days or %281_work%29%2F%2810_days%29 

x men's work rate = x times 1%2F90 or x%2F90

4 women's work rate = 4 times 1%2F120 or 4%2F120

So the equation comes from:

%28matrix%286%2C1%2C%0D%0Ax%2C%22men%27s%22%2Cwork%2Crate%2C+or%2C+x%2F90%29%29%22%22%2B%22%22%28matrix%286%2C1%2C%0D%0A4%2C%22women%27s%22%2Cwork%2Crate%2Cor%2C4%2F120%29%29 %22%22=%22%22 

x%2F90%22%22%2B%22%224%2F120 %22%22=%22%22 1%2F10

Reduce the fraction 4%2F120 to 1%2F30

x%2F90%22%22%2B%22%221%2F30 %22%22=%22%22 1%2F10

Multiply through by the LCD of 90

x + 3 = 9
    x = 6

So 6 men should work with the four women.

Edwin