At 6 am, there is a lot of activity in the corners. Three corners have three trains leaving at 6 am each, one horizontally, one vertically, and one diagonally. The northwest corner has four trains leaving at 6 am. Train stations are 10 minutes apart. It takes 10 minutes for a person to switch trains at a station.
Trains turn around at the terminus stations in negligible time.
You notice the diagonal lines and the line I've drawn with dashes. It's our best line, by the way. Now, Dr. Ecco, let me lay out the scenario. That takes 50 minutes. We've come to the right place.