You can set time limits for quizzes and then have open attempts automatically submit when the time runs out. While not exactly what you are purposing, I suppose you could use 1 of two workarounds:
- Divide the time you want for each question by the number of questions and set that for your quiz time. (For example, 5 questions with 10 minutes per question gives your quiz a total time of 50 minutes) They would be able to spend more time on some questions and less on others, but would still average 10 minutes per question.
- You could make separate quizzes for each question with the question time limit. Similar to the previous example, you would make 5 quizzes with 1 question each, each with a time limit of 10 minutes. Then, if the student isn't done at the 10 minute mark, it submits that quiz as a zero and then they can move on to the next question(quiz really) that has its own 10 minute time limit. The downside to this is you would get 5 individual grades instead of one cumulative one.