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Question 930275: A piece of work can be done by 6 men & 5 women in 6 days or 3 men & 4 women in 10 days. It can be done by 9 men & 15 women in ?
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website! OK--
Let t=amount of time it takes 9 men and 15 women to do the piece of work.
6 men and 5 women work at the rate of 1/6 of the piece of work per day
3 men and 4 women work at the rate of 1/10 of the piece of work per day
Let x=amount of time it takes a man working alone to do the piece of work
Then the man works at the rate of 1/x of the piece of work per day
Let y= amount of time it take a woman working alone to do the piece of work
Then the woman works at the rate of 1/y of the piece of work per day
soooo our equations to solve are:
6/x + 5/y=1/6----eq1
3/x + 4/y=1/10----eq2
Multiply eq2 by 2
6/x + 8/y=1/5 and subtract eq1
3/y=1/5-1/6=6/30 - 5/30=1/30
3/y=1/30;
y=90 days ---time it takes 1 woman to do the piece of work
substitute into eq1
6/x + 5/90= 1/6
6/x + 1/18=1/6 multiply by 18x
108+x=3x
2x=108
x=54 days ----time it takes 1 man to do the piece of work
(9/54 + 15/90)t=1 (1 piece of work, that is)
(3/18 +3/18)t=1
t/3=1
t=3 days
CK
In 3 days, 9 men do (9/54)*3=26/54 = 1/2 of the piece of work
In 3 days, 15 women do (15/90)*3=1/2 of the piece of work
Hope this helps---ptaylor
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