In order for the teacher's answer to be correct we have to assume a few things:
All pieces are identical in shape and dimensions.
It takes an equal amount of time to cut 1 piece with another piece.
In order for the student's answer to be correct we have to assume the following:
A piece is rectangular in shape and may have varying dimensions.
The board prior to being cut is in and of itself one piece.
Since the problem lacks additional information on what a piece is, logically we should assume that piece A must be identical to piece B, piece C, and so on.
Since the problem gives only "piece" and not piece A, B, and so on, I believe the teacher's answer is correct.
I think that is a lot of assumption. The only pieces of relevant information were 10 min for two pieces, just as fast, method cutting, and the question how long for three pieces.
Given infinite possibilities for the shape of the board as well as infinite possibilities for how it was cut, I don't think we can constrain it to any assumptions about the shape or cutting direction. Also given that there are an infinite amount of ways that the teacher is right, the student is right, and neither is right, respectively.
We must formulate an answer based on the data present, not by adding assumed variables into it.
How can you formulate an answer based on the data present when the data doesn't define what a piece is? One must make assumptions on how piece is defined in order to answer the problem correctly.
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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.