Three teachers were discussing how long they had been teaching.

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

Charlie and Billie 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?

Puzzle Copyright © Kevin Stone

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Hint

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

Answer

Alex had been teaching for 21 years.

Billie 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 + Billie + Charlie = 36 + 22 + 28 = 86.

So, Alex + Billie + 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 Billie 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 Billie must be: 43 - 28 = 15 years.

Alex and Billie 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, Billie = B and Charlie = C, then:

[1] A + B = 36

[2] C + B = 22

[3] C + A = 28

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

[4] A - B = 6

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

2A = 42

A = 21

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