Given multiple periods of time in a day, that may overlap, calculate the sum of all the periods, in hours.

example.php

<?php

$periods = [
    [new DateTime('8AM'), new DateTime('5PM')],   // 9 hours
    [new DateTime('8AM'), new DateTime('5PM')],   // 9 hours
    [new DateTime('10AM'), new DateTime('12PM')], // 2 hours
    [new DateTime('12PM'), new DateTime('5PM')],  // 5 hours
    [new DateTime('7PM'), new DateTime('8PM')],   // 1 hour
    [new DateTime('9AM'), new DateTime('4PM')],   // 7 hours
];

// Result: 10
echo total_hours_per_day($periods);

total_hours_per_day.php

<?php

/**
 * Calculates the total hours per day, considering period overlaps.
 * @param  array   $periods
 * @return integer
 */
function total_hours_per_day($periods)
{
    ksort($periods);
    do {
        $count = count($periods);
        foreach ($periods as $key1 => $period1) {
            foreach ($periods as $key2 => $period2) {
                if ($key2 > $key1 and $period1[0] <= $period2[1] and $period1[1] >= $period2[0]) {
                    $periods[] = [min($period1[0], $period2[0]), max($period2[1], $period1[1])];
                    unset($periods[$key1], $periods[$key2]);
                }
            }
        }
    } while ($count > count($periods));
    return array_reduce($periods, function ($total, $period) {
        return $total + $period[0]->diff($period[1])->h;
    });
}