Adi_Pat wrote:General strategy for a question where you're given the time taken to do a particular job by A & B together, B & C together and A&C together.

and asked to find the time taken by A,B and C together...

My approach ( which didnt work )

1/A + 1/B = Time (AB)
1/B + 1/C = Time (BC)
1/A + 1/C = Time (AC )

Time together = 1/A+1/B+1/C = { Time(AB) + Time(BC) + Time (AC) } / 2

Problem:
A and B take 56 hours to complete a job.
A and C take 40 hours to complete the same job.
B and C take 35 hours to complete the same job.
If A, B and C work together, how long would it take them to complete the job?

Solution:

When the job is undefined, plug in a number for the job.
In this problem, we need a multiple of 56=7*8, 40=5*8, and 35=5*7, so let's plug in that the job = 5*7*8 = 280.

Rate for A+B = work/time = 280/56 = 5/hour.
Rate for A+C = work/time = 280/40 = 7/hour.
Rate for B+C = work/time = 280/35 = 8/hour.

When people work together, we can add their rates. (If you stuff 2 envelopes per hour, and I stuff 3 envelopes per hour, our combined rate = 2+3 = 5/hour.)

Adding the equations above:
(A+B) + (A+C) + (B+C) = 5+7+8
2A + 2B + 2C = 20
A+B+C = 10
So combined rate for A+B+C = 10/hour.

Time for A+B+C = work/rate = 280/10 = 28.