Question 22761
Let M = one man and B = 1 boy.
If one man plus two boys can do the work in 12 days, then they can do 1/12 of the work in 1 day.
If three men and a boy can do the work in 6 days, then they can do 1/6 of the work in 1 day.

So we can write, for one day's work:

{{{M + 2B = 1/12}}} and
{{{3M + B = 1/6}}} 
 To find out how much of the work can be done in 1 day by 1 man (M), solve this system of equations for M:

Rewrite the second equation as {{{B = 1/6 - 3M}}} and substitute into the first equation.
{{{M + 2(1/6 - 3M) = 1/12}}} Simplify and solve for M.
{{{M + 1/3 - 6M = 1/12}}}
{{{-5M + 1/3 = 1/12}}} Subtract 1/3 (= 4/12) from both sides of the equation.
{{{-5M = -3/12}}} Divide both sides by -5.
{{{M = 3/60}}} Simplify.
{{{M = 1/20}}} This means that 1 man can do 1/20 of the work in 1 day. Therefore, it will take 1 man 20 days to do the entire job.