Subway debuted as Pete’s Super Submarines in Bridgeport, Conn., in the summer of 1965, when a Brooklyn-born 17-year-old named Fred DeLuca borrowed $1,000 from a family friend, a doctor named Peter Buck. De­Luca, an aspiring doctor who is now worth $2.6 billion, hoped slinging sandwiches would help him pay his way through medical school.

The duo slogged through several slow years of sandwich-making until, in 1974, they started selling franchises under a new name, Subway. (One theory: The old name, on radio ads, sounded confusingly like “Pizza Marines.”)

In the decades that followed those first shops, Subway franchises have expanded, yeast-like, onto what seemed like every street and strip mall in America. By 2013, Subway was opening 50 new shops a week. Today, Subways serves nearly 2,800 sandwiches every minute, data from industry researcher IBISWorld shows.

Still owned by Doctor’s Associates, the founders’ holding company, Subway has opened inside hundreds of…