- date_diff: documentation ( source)
<?php
$time1 = new DateTime('2018-10-01 13:00:00');
$time2 = new DateTime('2018-10-01 13:59:00');
$time3 = new DateTime('2018-10-01 14:29:00');
$time4 = new DateTime('2018-10-01 15:29:00');
$part1= date_diff($time2,$time1)->format('%h:%i:%s');
$part2= date_diff($time3,$time2)->format('%h:%i:%s');
$part3= date_diff($time4,$time3)->format('%h:%i:%s');
$part4 = (new DateTime('midnight'))
->add(date_diff($time2, $time1))
->add(date_diff($time4,$time3))
->diff(new DateTime('midnight'))
->format('%h:%i:%s');
echo $part4;