SOLUTION: 2 men and 5 women can together complete the work in 4 days while 3 mens and 6 women can finish it in 3 days .find the time taken by one man and women each to complete the work.

Question 488911: 2 men and 5 women can together complete the work in 4 days while 3 mens and 6 women can finish it in 3 days .find the time taken by one man and women each to complete the work.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
2 men and 5 women can together complete the work in 4 days while 3 mens and 6 women can finish it in 3 days .find the time taken by one man and women each to complete the work.
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Let a man's rate be "m"; Let a women's rate be "w":
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Equations:
2m + 5w = 1/4
3m + 6w = 1/3
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Modify:
8m + 20w = 1
9m + 18w = 1
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Modify:
72m + 180w = 9
72m + 144w = 8
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Subtract and solve for "w":
36w = 1
w = 1/36
Note: Since a woman's rate is 1/36 job/day,
a woman's time to do the job is 36 days/job.
+++++++++++++++++++++++++++++++++
Solve for "m":
9m + 18w = 1
9m + 18(1/36) = 1
9m + (1/2) = 1
9m = 1/2
m = 1/18
Note: Since a man's rate is 1/18 job/day,
a man's time to do the job is 18 days/job
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Cheers,
Stan H.
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