When I participated in the 2019 John Hopkins Math Tournament, the team round consisted of two separate topics, 40 minutes per round, and 3 people per team. My team suffered on the topology round. Only one team managed to get through more than a third of the round, and that was because one of their team members had taken topology before.
Now that I'm in college and actually taking topology, I decided to revisit the round. The questions are easy*, but 40 minutes for 13 problems, some of which contain multiple parts or subproblems, is just not enough time. I'm sure that even my professor would struggle to scribble down an answer for each question in reasonable detail within the time limit. With that being said, my specific question is as such: How long should the team round be to ensure that students with knowledge of set theory, but little to no prior knowledge of topology, would be able to solve at least half of the questions?
*In the sense that they serve as normal difficulty homework problems.