SOLUTION: 10 men and 15 women complete a job in 6 days, 1 man can complete the same work in 100 days, how many days does 1 women take to complete the same work

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Question 76623: 10 men and 15 women complete a job in 6 days, 1 man can complete the same work in 100 days, how many days does 1 women take to complete the same work
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The rate that the job is getting done by thge 10 men and 15 women
is 1 job / 6 days. I'll say that the rate that 1 man is doing the job
is 1%2Fm jobs/day and the rate that 1 woman is doing the job is
1%2Fw jobs/day.
10 men are working 10 times as fast and 15 women are working 15 times
as fast.
So, the rate 10 men are working is 10%2A%281%2Fm%29. The rate that
15 women are working is 15%2A%281%2Fw%29 therefore
1%2F6+=+10%2A%281%2Fm%29+%2B+15%2A%281%2Fw%29
The problem tells me that 1 man does the job in 100 days, so
1%2Fm+=+1%2F100
1%2F6+=+10%2A%281%2F100%29+%2B+15%2A%281%2Fw%29
1%2F6+=+1%2F10+%2B+15%2Fw
multiply both sides by the LCD, 30w
5w+=+3w+%2B+30%2A15
2w+=+450
w+=+225
So, 1%2Fw+=+1%2F225. It takes 1 woman 225 days to do the job alone.
check
1%2F6+=+10%2A%281%2F100%29+%2B+15%2A%281%2F225%29
1%2F6+=+1%2F10+%2B+1%2F15
5%2F30+=+3%2F30+%2B+2%2F30
OK