AA 3984 then AA 1044 at DFW
Rapid City → Dallas-Fort Worth → Louisville
Timetable, Dallas-Fort Worth time
16:35AA 3984 from Rapid City at the gate
09:39AA 1044 to Louisville leaves the gate
17 h 04 apart on the timetable, overnight
AA 1044 leaves 17 h 04 after AA 3984 arrives on the timetable: more than half a day, so not a connection we count.