Question 126265
{{{a}}} = time A takes
{{{b}}} = time B takes
{{{c}}} = time C takes
The sum of their rates is the final rate
1 job/a days + 1 job/b days + 1 job/c days = 1 job/6 days
{{{1/a + 1/b + 1/c = 1/6}}}
also given is
{{{1/b + 1/c = 1/9}}}
and
{{{1/a + 1/c = 1/8}}}
I need to find {{{a}}}, {{{b}}}, and{{{c}}}
I can directly substitute {{{1/b + 1/c = 1/9}}} 
into {{{1/a + 1/b + 1/c = 1/6}}}
{{{1/a + 1/9 = 1/6}}}
{{{1/a = 1/6 - 1/9}}}
{{{1/a = 3/18 - 2/18}}}
{{{1/a = 1/18}}}
{{{a = 18}}} answer
substituting,
{{{1/a + 1/c = 1/8}}}
{{{1/18 + 1/c = 1/8}}}
{{{1/c = 1/8 - 1/18}}}
{{{1/c = 9/72 - 4/72}}}
{{{1/c = 5/72}}}
{{{c = 14.4}}} answer
{{{1/b + 1/c = 1/9}}}
{{{1/b + 1/(72/5) = 1/9}}}
{{{1/b + 5/72 = 1/9}}}
{{{1/b = 1/9 - 5/72}}}
{{{1/b = 8/72 - 5/72}}}
{{{1/b = 3/72}}}
{{{b = 24}}} answer
A takes 18 days working alone, B takes 24 days working alone
and C takes 14.4 days working alone
check answers:
{{{1/a + 1/b + 1/c = 1/6}}}
{{{1/18 + 1/24 + 1/(72/5) = 1/6}}}
{{{4/72 + 3/72 + 5/72 = 12/72}}}
{{{12/72 = 12/72}}}
OK