Somewhere in the middle of the pool, Krystal Lara began to wonder when her hand would brush tile. She knew she was winning her race, but like most backstrokers in unfamiliar waters, she had only a vague sense of how far she had left to go. With her face cocked upward, she discerned her progress by the overhead lights retreating out of sight in a fluorescent blur.

When her fingertips finally touched the end of the pool, at the Greensboro Aquatic Center in North Carolina last August, Krystal heard her teammates break into rapturous applause. She slid on her glasses and the figures on the scoreboard came into focus: 1:03.28 — just fast enough to qualify for the 100-meter event at the Olympic trials in Omaha this summer. Scanning the crowd of frenzied faces, Krystal locked eyes with her mother. The two exchanged a look of disbelief before breaking into tears.

“I just felt this huge sense of pride,” Krystal, now an 18-year-old senior at Stuyvesant High School in Lower Manhattan, recalled. “Like all this work and all we’d been through had been worth it.”

Her mother, Alexandra Lara, remembered turning to the person next to her in the stands to explain her tears. “You don’t understand how hard it is for a family like ours to have this result,” she said.