Thoughts on how to make it easier/faster for students to switch classrooms.

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So I’ve been thinking about minimizing the time it takes for all of the students to change classes. This is a very difficult problem because there are so many people with so many variables. We would assume, however, that all of the kids in a given class would be going to the same classroom. It seems like the best way would be to maximize the average velocities of the individuals. What makes this problem difficult is that the velocity of each student in the hallway is inversely proportional to the number of students in the hallway at that given time. This makes the problem very dynamic. We would need to figure out what the relationship is between the time it takes for a given student to get to his/her class is as a function of the number of kids in the hallway. We would find the time it would take them to walk from their starting to ending point without anyone in the hallway and then the time it took with a given number of people trying to do the same thing. In fact, we could start with x people each with their maximum time values already known (the time it took them to get from their initial to final without anyone in the hallway) and then run experiments where we increase the number of people. We could then graph the time it took each individual as a function of the number of people in the hallway and find the relation. We would hopefully have enough data to find a relation and we could determine constants of the regression.