A rapid spell with a casting time measured in rounds can be cast in 1 full round. Rapid spells with casting times measured in minutes can be cast in 1 minute, and rapid spells with casting times measured in hours can be cast in 1 hour.
But since it also says that "Only spells with a casting time greater than 1 standard action can be made rapid," which a spell with a 1 minute casting time clearly is, I'd suggest that your DM treat it as though the casting time were 10 rounds (which is the equivalent of 1 minute), since it's clearly supposed to cover spells like the one you're talking about.
