Question 881575
y = man rate
x = woman rate


{{{3y*9+6x*9=1}}}, the first combination described
{{{27y+54x=1}}}


{{{2y*12+8x*12=1}}}, the second combination described
{{{24y+96x=1}}}


First combination,
{{{27y=1-54x}}}
{{{y=(1-54x)/27}}}
substitute into second combination,
{{{24(1-54x)/27+96x=1}}}
{{{24(1-54x)+96*27x=27}}}
{{{24-27*54x+27*96x=27}}}
{{{27*96x-27*54x=3}}}
{{{27(96x-54x)=3}}}
{{{42x=3/27}}}
{{{x=(1/9*42)}}}
{{{highlight(x=1/378)}}}, meaning one woman does 1 job in 378 days working alone.


Man rate: {{{y=(1-54x)/27}}}
{{{y=(1-54/378)/27}}}
{{{y=(1-(9*3*2)/(9*2*3*7))/27}}}
{{{y=(1-1/7)/27=(7/7-1/7)/27}}}
{{{y=6/(7*27)}}}
{{{highlight(y=2/63)}}}, the one man rate, two jobs in 63 days working alone.


To answer the question, the expression for 12 women doing the one job will be
Let t = time in days;
{{{highlight(highlight(12(1/378)*t=1))}}}
Solve for t.