In the 3,200-metre state championship race, Meghan Vogel, 17, was rounding the final lap with the finish line in sight when another runner collapsed in front of her. She could have run on. They were the last runners in the race, and as Ms. Vogel’s mom explained later, her daughter – who had won the 1,600-metre race with a personal best an hour earlier – had never finished in last place in a race before.