Canoe trip back to camp against a 2 mph current

Some friends leave their campsite by canoe, paddling upstream for $3$ hours. They then turn and paddle downstream for $5$ hours, finishing $32$ miles downstream of the campsite. The river runs downstream at a steady $2$ mph and their paddling speed in still water is constant. The following morning they paddle upstream back to the campsite, reaching it at 7:00 PM. At what time did they set off? Give the time as a 24-hour number without a colon (e.g. 4:30 AM is $430$, 4:30 PM is $1630$).

1340. With still-water speed $x$, net displacement is $3(x-2)-5(x+2)=-32$, so $x=8$ mph. Going upstream at $6$ mph, $32$ miles takes $5\tfrac13$ hours, i.e. 5 h 20 min, so they left at 1:40 PM.