MySQL 8.0

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CREATE TABLE test (
  id INT(11) DEFAULT NULL,
  time_event DATETIME NOT NULL,
  is_work INT(1) NOT NULL
);
INSERT INTO test (id, time_event, is_work) VALUES
(1, '2019-01-03 08:39:02',1), 
(1, '2019-01-03 08:40:02',1), 
(1, '2019-01-03 08:40:32',1),
(1, '2019-01-03 08:41:30',1),
(1, '2019-01-03 08:42:30',1),
(1, '2019-01-03 08:42:46',0), 
(1, '2019-01-03 08:42:58',0),
(1, '2019-01-03 08:46:49',0),
(1, '2019-01-03 08:47:11',0),
(1, '2019-01-03 08:53:47',1),
(1, '2019-01-03 08:54:47',1),
(1, '2019-01-03 08:55:47',1),
(1, '2019-01-03 08:56:47',1),
(1, '2019-01-03 08:57:35',1),
(1, '2019-01-03 08:58:35',1);
WITH 
cte1 AS ( SELECT id,
                 time_event, 
                 is_work,
                 LAG(is_work) OVER (PARTITION BY id 
                                     ORDER BY time_event ASC) work_prev, 
                 LEAD(is_work) OVER (PARTITION BY id 
                                     ORDER BY time_event ASC) work_next
          FROM test ),
cte2 AS ( SELECT id,
                 time_event,
                 SUM(work_next) OVER (PARTITION BY id
                                      ORDER BY time_event ASC) group_num
          FROM cte1
          WHERE is_work = 1 
            AND COALESCE(work_prev, 0) + COALESCE(work_next, 0) = 1 )
SELECT CONCAT( 'Агрегат ID = ', 
               id, 
               '. Работал с ', 
               MIN(time_event), 
               ' по ',
               MAX(time_event),
               '. Общее время работы - ',
               TIMEDIFF(MAX(time_event), MIN(time_event)),
               ' .') output
FROM cte2
GROUP BY id, group_num
ORDER BY id, group_num;


output


Агрегат ID = 1. Работал с 2019-01-03 08:39:02 по 2019-01-03 08:42:30. Общее время работы - 00:03:28 .

Агрегат ID = 1. Работал с 2019-01-03 08:53:47 по 2019-01-03 08:58:35. Общее время работы - 00:04:48 .