2 women and 7 girls can do a peice of work in 4 days. 4 women and 4 girls can do the same work in 3 days. How long would it take for 1 women and 1 girl to do the work.

x: work a woman can do in 1 day

y: work a girl can do in 1 day

Then

2x + 7y = 1/4

4x + 4y = 1/3

4x + 14y = 2/4 (1)

4x + 4y = 1/3 (2)

=> Let (1) - (2), 10y = 2/4-1/3 10y = 1/6 y = 1 / (6x10) = 1/60 (work)

=> From (2),4x = 1/3 - 4x1/60 = > 4x = 16/60 = > x = 4/60 (work)

=> 1 day, a woman and a girl can do: 1/60+4/60 = 5/60 = 1/12 (work)

Then, the day required for a woman and a girl to complete work: 12 days