SOLUTION: Hi 10 men and 20 women can do a job in 15 days. 15 men and 10 women can do the same job in 20 days. 1 man can complete the job in how many days. Thanks

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Question 1149035: Hi
10 men and 20 women can do a job in 15 days. 15 men and 10 women can do the same job in 20 days. 1 man can complete the job in how many days.
Thanks
Answer by VFBundy(438) About Me  (Show Source):
You can put this solution on YOUR website!
Set up two equations. The reason the equations end with fractions is because that is the fraction of work PER DAY that these combinations of men and women can do.

10M + 20W = 1/15
15M + 10W = 1/20

Since we are looking for how long it takes 1 man do to the work, we want to eliminate women (W) from the equation. Start by multiplying the second equation by -2:

-2(15M + 10W) = -2(1/20)
-30M - 20W = -1/10

Now, here are your two equations:

10M + 20W = 1/15
-30M - 20W = -1/10

Add the two equations together and solve for M:

-20M = -1/30

M = 1/600

So...if 1 man can do 1/600 of the job per day, that means it will take him 600 days to do the job.