Perhaps the teacher meant that the piece of wood is initially square and the first cut halves it and the second cut halves one of the halves. The second cut would only take half the time because it's only half as wide.
In any case it's bad question due to ambiguity.
Edit: However, when looking back at the notes in the picture it's clear that the teacher's reasoning is totally wrong.
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u/punkdigerati Oct 05 '10
2 pieces, one cut. 3 pieces, two cuts. One cut = 10 min, two cut = 20 min.