SOLUTION: 12 men complete the job in 6 days, 10 men and 21 women complete the same job in 3 days. how many days will require for 12 women to complete same job.

Algebra ->  Rate-of-work-word-problems -> SOLUTION: 12 men complete the job in 6 days, 10 men and 21 women complete the same job in 3 days. how many days will require for 12 women to complete same job.       Log On


   

Question 894307: 12 men complete the job in 6 days, 10 men and 21 women complete the same job in 3 days. how many days will require for 12 women to complete same job.
Answer by josgarithmetic(39627) About Me  (Show Source):
You can put this solution on YOUR website!
R rate for 1 man
r rate for 1 woman

12%2AR%2A6=1; %2810R%2B21r%29%2A3=1 because their rates are summed when working together.
These two equations are a system using the two variables, r and R.
Use the first one to find R, and use this now known R to find the value for r.

R=1%2F%2812%2A6%29
highlight_green%28R=1%2F72%29
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%2810%2F72%2B21r%29%2A3=1
10%2F24%2B63r=1
63r=1-10%2F24
63r=1-5%2F12=12%2F12-5%2F12
63r=7%2F12
r=7%2F%2863%2A12%29
r=1%2F%289%2A12%29
highlight_green%28r=1%2F108%29
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The question is, how many days (t = time in DAYS) for 12 women to do 1 job?

12%281%2F108%29%2At=1
t=108%2F12
highlight%28t=9%29 DAYS