How long will it take Marie to saw another board into 3 pieces? So this is supposed to be really simple, and it's taken from the following picture:

Text-only:

It took Marie $10$ minutes to saw a board into $2$ pieces. If she works just as fast, how long will it take for her to saw another board into
  $3$ pieces?

I don't understand what's wrong with this question.  I think the student answered the question wrong, yet my friend insists the student got the question right.
I feel like I'm missing something critical here. What am I getting wrong here?

The student is absolutely correct (as Twiceler has correctly shown).
The time taken to cut a board into $2$ pieces (that is $1$ cut) : $10$ minutes
Therefore, The time taken to cut a board into $3$ pieces (that is $2$ cuts) : $20$ minutes
The question may have different weird interpretations as I am happy commented:<br

Time taken to cut it into one piece = $0$ minutes
So Time taken to cut it into $3$ pieces = $0 \times 3$ minutes = $0$ minutes.

So $0$ can be an answer. but it is illogical just like the teacher's answer
and as Keltari said

Another correct answer would be 10 minutes. One could infer, "If she works just as fast," that "work" is the complete amount of time to do the job.  -Keltari

This is logical but you can be sure that this is not what the question meant, but the student has chosen the most relevant one. The teacher's interpretation is mathematically incorrect. 
The teacher may have put the question for the students to have an idea of Arithmetic Progression and may have thought that the students will just answer the question without thinking hard. In many a schools, at low grades children are thought that real numbers consists of all the numbers. Only later in higher grades do they learn that complex numbers also exist. (I learned just like that.) So the question was put as a question on A.P. thinking that the students may not be capable of solving the answer the correct way.
Or as Jared rightly commented:

This is simultaneously wonderful and sad. Wonderful for the student who was level-headed enough to answer this question correctly, and sad that this teacher's mistake could be representative of the quality of elementary school math education. – Jared

Whatever may be the reason, there is no doubt that the student has been accurate in answering the question properly and that the teacher's answer is illogical.
