As usual, once I've asked the question, I find the answer myself.
However, it *feels* like there should be a more efficient way. Can anyone 
comment or suggest a better method?
timetable=> select stts_id, stts_offset+stts_duration as total_duration 
timetable-> from standard_trip_sections 
timetable-> where (stts_id, stts_offset) in 
timetable-> (select stts_id, max(stts_offset) from standard_trip_sections 
group by stts_id);
 stts_id | total_duration 
---------+----------------
       1 | 01:35:00
       2 | 01:35:00
       3 | 01:08:00
       4 | 01:38:00
       5 | 01:03:00
       6 | 01:06:00
(6 rows)
timetable=>