AA 9909 then UA 6059 at Denver
Los Angeles → Denver → Hays
Timetable, Denver time
16:45AA 9909 from Los Angeles at the gate
16:20UA 6059 to Hays leaves the gate
23 h 35 apart on the timetable, overnight
UA 6059 leaves 23 h 35 after AA 9909 arrives on the timetable: more than half a day, so not a connection we count.