The question does not say cut "into thirds," it says "into three pieces." This - http://i.stack.imgur.com/kEjP0.png - is a perfectly reasonable answer which, assuming the rate of cutting is constant, would result in 15 minutes.
It's a bad question.
Edit: That said, I would have given the same answer as the student, because I think that's the most reasonable interpretation, especially considering the illustration. But the keyword there is "interpretation." The question is ambiguous.
The question does not say cut "into thirds," it says "into three pieces." This - http://i.stack.imgur.com/kEjP0.png - is a perfectly reasonable answer which, assuming the rate of cutting is constant, would result in 15 minutes.
It's a bad question.
Edit: That said, I would have given the same answer as the student, because I think that's the most reasonable interpretation, especially considering the illustration. But the keyword there is "interpretation." The question is ambiguous.
(My argument is taken from this answer: http://math.stackexchange.com/a/380007 )