This question is almost totally unanswerable unless you clarify what is meant by "basic arithmetic problems for kids and teens".
But let's consider a lower-bound case where you're talking about basic one-digit addition and multiplying facts. In instances like this, the knowledge should be automatic, that is, instantly recalled without effort (at least by the 3rd grade).
A few years ago, when developing a similar gamey practice website (Automatic-Algebra.org), I made a survey of several educators' and practice materials' suggestions for times-tables drills. That's summarized in the chart below:
In short: Simple times-tables facts should be answerable in 2 or 3 seconds on average. Personally, I set up my drill to give twice that much time as a safety buffer (30 seconds for 5 questions, that is, one every 6 seconds).
Best practice would be to test and refine your game with actual users. In the most general sense, questions might take anywhere between zero and infinity seconds, depending on what you're asking.