SOLUTION: 3 men and 6 women finish a job in 9 days while 2 men and 8 women finish it in 12 days.in hie many days will 12 women working alone will finish the same job

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Question 881575: 3 men and 6 women finish a job in 9 days while 2 men and 8 women finish it in 12 days.in hie many days will 12 women working alone will finish the same job
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
y = man rate
x = woman rate

3y%2A9%2B6x%2A9=1, the first combination described
27y%2B54x=1

2y%2A12%2B8x%2A12=1, the second combination described
24y%2B96x=1

First combination,
27y=1-54x
y=%281-54x%29%2F27
substitute into second combination,
24%281-54x%29%2F27%2B96x=1
24%281-54x%29%2B96%2A27x=27
24-27%2A54x%2B27%2A96x=27
27%2A96x-27%2A54x=3
27%2896x-54x%29=3
42x=3%2F27
x=%281%2F9%2A42%29
highlight%28x=1%2F378%29, meaning one woman does 1 job in 378 days working alone.

Man rate: y=%281-54x%29%2F27
y=%281-54%2F378%29%2F27
y=%281-%289%2A3%2A2%29%2F%289%2A2%2A3%2A7%29%29%2F27
y=%281-1%2F7%29%2F27=%287%2F7-1%2F7%29%2F27
y=6%2F%287%2A27%29
highlight%28y=2%2F63%29, the one man rate, two jobs in 63 days working alone.

To answer the question, the expression for 12 women doing the one job will be
Let t = time in days;
highlight%28highlight%2812%281%2F378%29%2At=1%29%29
Solve for t.