value from max row in group by

Hi folks,

I need help please.

I have a table of trip section details which includes a trip ID, start time as 
an offset, and a duration for that section.

I need to extract the full trip duration by adding the highest offset to it's 
duration. I can't simply use sum() on the duation as that would not include 
standing time.

Using the data below I would like to get:

1  | 01:35:00
2  | 01:35:00
3  | 01:06:00
4  | 01:38:00
5  | 01:03:00
6  | 01:06:00

from 

timetable=> select stts_id, stts_offset, stts_duration from 
standard_trip_sections order by stts_id, stts_offset;stts_id | stts_offset | stts_duration 
---------+-------------+---------------      1 | 00:00:00    | 00:18:00      1 | 00:19:00    | 00:26:00      1 |
00:47:00   | 00:13:00      1 | 01:13:00    | 00:22:00      2 | 00:00:00    | 00:18:00      2 | 00:20:00    | 00:09:00
  2 | 00:29:00    | 00:17:00      2 | 00:50:00    | 00:13:00      2 | 01:13:00    | 00:22:00      3 | 00:00:00    |
00:20:00     3 | 00:28:00    | 00:15:00      3 | 00:44:00    | 00:22:00      3 | 00:48:00    | 00:20:00      4 |
00:00:00   | 00:20:00      4 | 00:28:00    | 00:15:00      4 | 00:48:00    | 00:13:00      4 | 01:01:00    | 00:13:00
  4 | 01:18:00    | 00:20:00      5 | 00:00:00    | 00:18:00      5 | 00:20:00    | 00:09:00      5 | 00:29:00    |
00:17:00     5 | 00:50:00    | 00:13:00      6 | 00:00:00    | 00:15:00      6 | 00:20:00    | 00:13:00      6 |
00:33:00   | 00:13:00      6 | 00:46:00    | 00:20:00
 
(26 rows)

timetable=>