Question 983773
R rate of 1 man
r rate of 1 woman

{{{system(12R*10=1,20r*12=1)}}}
-
{{{system(R=1/120,r=1/240)}}}


Let t be the time needed to complete after some of the job was done using the described combination of men and women.


{{{8(1/120)*10+4(1/240)*10+8(1/120)t+(4+10)(1/240)t=1}}}
Simplify this and solve for t.


{{{80/120+40/240+8t/120+14t/240=1}}}


{{{8/12+4/24+(8/120)t+(7/120)t=1}}}

{{{2/3+1/6+(2/30)t+(7/120)t=1}}}

LCD is 120.
Multiply LCD by both sides.

{{{80+20+8t+7t=120}}}

{{{15t=120-80-20}}}

{{{15t=20}}}

{{{t=20/15}}}

{{{highlight(t=4/3=1&1/3)}}}, this many days.