SOLUTION: A particular work can be completed by 6 men and 6 women in 24 days. Whereas the same work can be completed by 8 men and 12 women in 15 days. Find the amount of work done, one men

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Question 955988: A particular work can be completed by 6 men and 6 women in 24 days. Whereas the same work can be completed by 8 men and 12 women in 15 days. Find the amount of work done, one men is equivalent to how many Women.
Answer by josgarithmetic(39615) About Me  (Show Source):
You can put this solution on YOUR website!
Rates are as JOB per DAY, or 1%2F%28howManyDays%29.

R rate for 1 man
r rate for 1 woman
1, the amount of work for the expected 1 job.

particular work can be completed by 6 men and 6 women in 24 days.
%286R%2B6r%29%2A24=1

the same work can be completed by 8 men and 12 women in 15 days.
%288R%2B12r%29%2A15=1

Simplify the two equations.
-
6%2A24R%2B6%2A24r=1
144R%2B144r=1
-
8%2A15R%2B12%2A15r=1
120R%2B180r=1

System to solve:
system%28144R%2B144r=1%2C120R%2B180r=1%29

Substitution would be an easier method than elimination . Maybe.

180r=1-120R
highlight_green%28r=%281-120R%29%2F180%29
-
144R%2B144%281-120R%29%2F180=1
144%2A180%2AR%2B144%281-120R%29=180
144%2A180R%2B144-120%2A144R=180
144%2A180R-120%2A144R=180-144
144R%28180-120%29=36
144%2A60R=36
24%2A10R=1
highlight%28R=1%2F240%29------One man does one job in 240 days.

r=%281-120R%29%2F180
r=%281-120%281%2F240%29%29%2F180
r=%281%2F2%29%2F180
highlight%28r=1%2F360%29------One WOMAN does one job in 360 days.

If n is the number of women to make the rate of work for 1 man, then
n%281%2F360%29=1%2F240
n=360%2F240
n=36%2F24
n=6%2F4
highlight%28n=3%2F2%29
--------One man is equivalent to highlight%281%261%2F2%29 women.