Mysql select copy column to another, id no successive

Question

i want to get the interval of time of every event in all the areas of my work place, so i got this table that shows the time an event ocurr

ID | area |   TIME 1
01 |  A   |  2016-09-20 14:55:54 
02 |  A   |  2016-09-21 18:00:00
04 |  A   |  2016-09-23 20:14:14
06 |  B   |  2016-09-24 13:52:24
10 |  B   |  2016-09-26 13:33:34
13 |  B   |  2016-09-28 18:22:46

as we can see, the id is not successive because there's another data filtered in the query, i want the output to be like this:

area |          TIME 1       |       TIME 2
 A   |  2016-09-20 14:55:54  | 2016-09-21 18:00:00
 A   |  2016-09-21 18:00:00  | 2016-09-23 20:14:14
 B   |  2016-09-24 13:52:24  | 2016-09-26 13:33:34
 B   |  2016-09-26 13:33:34  | 2016-09-28 18:22:46

is there a way to do it in the select?, i use a inner join to the same "time 1", but it gets the "time 2" for every "time 1" resulting in, for area A:

    area |          TIME 1       |       TIME 2
     A   |  2016-09-20 14:55:54  | 2016-09-20 14:55:54
     A   |  2016-09-20 14:55:54  | 2016-09-21 18:00:00
     A   |  2016-09-20 14:55:54  | 2016-09-23 20:14:14
     A   |  2016-09-21 18:00:00  | 2016-09-20 14:55:54
     A   |  2016-09-21 18:00:00  | 2016-09-21 18:00:00
     A   |  2016-09-21 18:00:00  | 2016-09-23 20:14:14
     A   |  2016-09-23 20:14:14  | 2016-09-20 14:55:54
     A   |  2016-09-23 20:14:14  | 2016-09-21 18:00:00
     A   |  2016-09-23 20:14:14  | 2016-09-23 20:14:14

Answer 1

SQL Fiddle Demo

SELECT *
FROM Table1 T1
JOIN Table1 T2
  ON T1.area = T2.area 
 AND T2.ID = (SELECT MIN(T3.ID) 
              FROM Table1 T3
              WHERE T3.ID > T1.ID
                AND T3.area = T1.area)

OUTPUT

EDIT : I assume if ID_1 < ID_2 then Time_1 < Time_2