I Can. Can You?

I learned how to say 'I can' in Japanese when I first studied the language in 2005. It turned out to be an experience that I will not easily forget.
I had to go through the whole thing again some weeks ago when we were studying 'dekiru', or 'to be able to', here at APU. Here's what happened both times:

Teacher: Lee-san, can you swim?
Lee: No.
Teacher and all the Westerners: EH? Really?
Teacher: Obunshu-san, can you sw...
Obunshu-san: No.
Teacher: Eh? Oh. Ming-san, can you...
Ming-san: No.
Teacher: Cheng-san, c...
Cheng-san: No.
Obunhin-san (who sits next to Cheng-san): No.
Teacher: EH? Everyone, can you not swim?
Chinese kids: No!

And as if that wasn't strange enough, the next step really did it. How was I supposed to answer that question?

Teacher: Solveig-san, can you swim?
Me, feeling weird at being the first to say that: Yeees.
Teacher: How far can you swim?
Me: ???!!!! Eh?
Teacher: How many meters can you swim, approximately?
Me, getting really nervous, because I really don't know the answer. What does she mean? How far can I swim before I can't do it anymore and drown? I usually give up because it's boring :P But really. When you swim, you take breathers. So here's what I said, thinking of "ég ætla að synda 500 metrana": I, I don't know... 500 maybe?
Teacher and Class: Eeh? Wow! That's amazing!
Me feeling really really weird becomes really glad that there are other Western people in the class that can swim too, most of them more than I do.

That is one of the weirdest classes I have had. And I got it twice!! I was prepared this time, but it was still strange and I felt weird.
Here's another question about 'dekiru', this time from the book we use:
まいにち　じかん　にほん　ご
毎日３時間日本語のべんきょうをすることができますか。
mai nichi san ji kan nihongo no benkyou wo suru koto ga dekimasu ka?
'Can you study Japanese for 3 hours every day?'
What is it really asking about?