The running world has a habit of turning older marathoners into mascots. Who doesn’t love the story of the great-grandfather who gets across the finish line in seven hours?

But with all due respect to that sort of wrinkled runner, 75-year-old Hernán Barreneche Rios isn’t traveling to Sunday’s New York City Marathon from his home in Colombia to simply get a medal for participation. The retired professor of mechanical engineering is looking to break 3 hours, 30 minutes and win his division—just like he did last year when he...