The student's answer is a beautiful demonstration of linear thinking in a non-linear world! They've assumed that if 10 minutes = 2 pieces, then 15 minutes = 3 pieces. But they missed the crucial detail—cutting a board into 2 pieces requires ONE cut, while cutting it into 3 pieces requires TWO cuts!
This is basically the mathematical equivalent of thinking you can cook two chickens in the same time as one chicken. The correct answer is 20 minutes (2 cuts × 10 minutes per cut). Math teachers everywhere are silently screaming into their coffee mugs right now.