This is lovely! To quote Isaac Newton what we have here is not a mathematical problem. The question is, what is the mathematical problem.
So far as I can see, the most logical interpretation of the question is that there exists a standard task T, and on different occasions three diferent teams, A + B, A + C and B + C complete T in different times. From this we have to work out how long each individual would take to complete T, working on his own.
If you accept this as the mathematical problem then pilotmike has the mathematical answer.
Remember that Godel said that in any formal mathematical system there are theorems that are true that cannot be proved within that system.
and vice versa!
Dick