Puzzle ZKLD 

Workings

Hint
Alex had been teaching 6 years longer than Blake.

Answer
Alex had been teaching for 21 years.
Blake had been teaching for 15 years.
Charlie had been teaching for 7 years.

Alex and Blake had been teaching for a total of 36 years.

Charlie and Blake had been teaching for a total of 22 years.

Charlie and Alex had been teaching for a total of 28 years.

Let Alex = A, Blake = B and Charlie = C, then:

   A + B = 36       [1]
   C + B = 22       [2]
   C + A = 28       [3]

If we use [3] - [2] we have:

   A - B = 6        [4]

If we use [1] + [4] we have:

   2A = 42
    A = 21

By [1] B = 15. By [3] C = 7.