How many days will 15 women and 5 men take to do it?

Question

If 11 men and 16 women can do a piece of work in 6 days and 7 men and 9 women can do it in 10 days.
How many days will 15 women and 5 men take to do it?

Answer 1

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 +15 women to complete work, then we have:
1) 11m+16w=1/6
2) 7m+9w=1/10
3) 5m+15w=1/x

From 1) and 2) we find that
66m+96w=1, 70m+90w=1-> 4m=6w
m=1/130
w=1/195
x=1/(5m+15w)=8 2/3 days
x= 8 2/3 days