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

Overlap.php

<?php
//24 hours in one day, plus an extra hour to count any minutes past midnight
$totals = array_fill_keys(range(0, 24), array_fill_keys(range(0, 59), 0));

//loop through the ranges
foreach ($ranges as $range) {
    $start = (int) $range[0]->format('H');

    //the duration of this range
    $delta = $range[1]->diff($range[0]);

    //the minutes
    $start_range = array_fill_keys(range((int) $range[0]->format('i'), 59), 1);
   
    $totals[$start] = $start_range + $totals[$start];
    for ($a = 1; $a < $delta->h; $a++) {

        $totals[$start + $a] = array_fill_keys(range(0, 59), 1);
    }

    $end_range = array_fill_keys(range(1, (int) $range[1]->format('i')), 1);
    $totals[$start + $a] = $end_range + $totals[$start + $a];
}



$hours = 0;
$minutes = 0;

foreach ($totals as $total) {
    $duration = array_sum($total);
    
  
    //if duration is 60 seconds or more, this hour is full
    if ($duration >= 60) {
        $hours += 1;
    } else {
        //otherwise, count the minutes
        $minutes += $duration;
    }
}

//if we have over 60 seconds of spare minutes, these are also hours
$hours += intval($minutes / 60);
$minutes = $minutes % 60;