Question 85255
1.  Create a system of equations based on what portion of the job each group can do in 1 day:

A + B + C = {{{1/6}}} [together, they can do {{{1/6}}} of the job per day]
    B + C = {{{1/9}}} [together, B and C can do {{{1/9}}} of the job per day]
A +     C = {{{1/8}}} [together, A and C can do {{{1/8}}} of the job per day]

Combine the first two equations to eliminate B and C and solve for A:

A + B + C = {{{1/6}}}
    -B - C = -{{{1/9}}}
________________________
A          = {{{3/54}}}
A alone can do {{{3/54}}} of the job per day so it'll take A {{{54/3}}} = 18 days to do the job alone
Now, plug {{{3/54}}} or {{{1/18}}} into the third equation for A and solve for C:
{{{1/18}}} + C = {{{1/8}}}
C = {{{1/8}}} - {{{1/18}}} = {{{5/72}}}
C alone can do {{{5/72}}} of the job per day so it'll take C {{{72/5}}} = 14{{{2/5}}} days to do the job alone
Now, plug 5/72 into the second equation for C and solve for B:
B + {{{5/72}}} = {{{1/9}}}
B = {{{1/9}}} - {{{5/72}}} = {{{3/72}}}
B alone can do {{{3/72}}} of the job per day so it'll take B {{{72/3}}} = 24 days to do the job alone