Question

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.

Answer 1

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