Question 140876
b and c working together take 9 days to do {{{1}}} job
b and c working together take 3 days to do {{{1/3}}} job
b and c working together take 6 days to do {{{2/3}}} job
a, b and c working together take 6 days to do {{{1}}} job
So, a must do {{{1 - 2/3 = 1/3}}} of a job in {{{6}}} days
a and c working together take {{{8}}} days to do {{{1}}} job
a and c working together take {{{2}}} days to do {{{1/4}}} job
a and c working together take {{{6}}} days to do {{{3/4}}} job
Since a does {{{1/3}}} job in {{{6}}} days, 
c does {{{3/4 - 1/3 = 5/12}}} of a job in {{{6}}} days
{{{(1/3)/6 + (b)/6 + (5/12)/6 = 1/6}}}
{{{1/3 + b + 5/12 = 1}}}
{{{b = 12/12 - 4/12 - 5/12}}}
{{{b = 3/12}}}
{{{b = 1/4}}}
So, b does {{{1/4}}} of a job in {{{6}}} days
The question I need to answer is how long does it take each man,
working alone, to do {{{1}}} job?
If a does {{{1/3}}} of a job in {{{6}}} days, 
he will do {{{1}}} job in {{{3*6 = 18}}} days answer
If b does {{{1/4}}} of a job in {{{6}}} days
he will do {{{1}}} job in {{{4*6 = 24}}} days answer
If c does {{{5/12}}} of a job in {{{6}}} days
he will do {{{1}}} job in {{{(12/6)*6 = 14.4}}} days answer
check answer:
{{{1/18 + 1/24 + 1/14.4 = 1/6}}}
{{{.0555 + .041666 + .069444 = .1666}}}
{{{.1666 = .1666}}}
OK