I obviously thought 15 min when I first read it and my brain didn't want to accept any other solution until I read the post below where it said 20 min and explained it as 2 pieces = 1 cut = 10 min, 3 pieces = 2 cuts = 20 min.
And now I can't see why my first thought was correct. Did you come up with some good rationale as to why it should be 15 min or other?
Because it depends on whether you 1) require that the N pieces be congruent and 2) what counts as a cut. I think the textbook answer is based on assuming 1) no, and 2) cutting along a line segment at least as long as a side.
Alternately, what counts as a "board" and a "cut".
Then you get the answer by assuming you cut a square board in half, then one of the pieces into squares (which requires cutting along a line segment half as long).
The problem does specify 'works as fast' without any regard for length, though. And it obviously isn't actually a geometry problem because it doesn't even specify any ratios or angles - you could just cut a corner off and be done in a few seconds!
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If it was dressed, that 1 might be very small indeed.