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?
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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.
