How many days will 5 men and 12 women take to do it?

Question

If 6 men and 10 women can do a piece of work in 15 days and 5 men and 9 women can do it in 17 days.
How many days will 5 men and 12 women take to do it?

Answer 1

13.6 days

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Let the work be =1, man's work for one day =m, woman's work for one day =w and x= the number of days required for 5 men +12 women to complete work, then we have:
1) 6m+10w=1/15
2) 5m+9w=1/17
3) 5m+12w=1/x

From 1) and 2) we find that
90m+150w=1, 85m+153w=1-> 90m=150w=85m+153w-> 5m=3w
2)5m+9w=12w=1/17, w=1/204
3)5m+12w=3w+12w=15w=1/x,
x=1/15w=1/(15*1/204)=13.6
x= 13.6 days