 # Puzzle ZKLD  ?

Three teachers were discussing how long they had been teaching.

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.
How long had each been teaching?

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

Reasoning
If we look at all of the clues, each person appears exactly twice.

So the total of the three clues gives us two lots of Alex + Blake + Charlie = 36 + 22 + 28 = 86.

So, Alex + Blake + Charlie = 43 years.

In each clue we are given two of the people, so we can use this to find the missing person:

Charlie and Blake had been teaching for a total of 22 years, which means that Alex must be: 43 - 22 = 21 years.

Charlie and Alex had been teaching for a total of 28 years, which means that Blake must be: 43 - 28 = 15 years.

Alex and Blake had been teaching for a total of 36 years, which means that Charlie must be: 43 - 36 = 7 years.

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

   A + B = 36
   C + B = 22
   C + A = 28

If we use  -  we have:

   A - B = 6

If we use  +  we have:

2A = 42
A = 21

By  B = 15. By  C = 7.

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