Question 451900
{{{1/a + 1/b = 23/318}}}

{{{1/b + 1/c = 5/66}}}

{{{1/a + 1/c = 23/396}}}

Subtracting the 2nd equation from the 1st, we get {{{1/a - 1/c = -2/583}}}.

Adding the previous equation to the 3rd equation gives  {{{2/a = 1147/20988}}}.

==> {{{a/2 = 20988/1147}}} ==> {{{a = 41976/1147 = 36&684/1147}}} hours.  
You can now get the values for b and c.