If you can use an open JavaScript library like moment.js, the following is simple and preserves your string formatted times.

Note that I'm passing in "00:00" as the default value to reduce() so that times are calculated from a zero baseline, which also follows the string formatting that we'll use for all other values in the array.

const times["00:30", "01:45", "02:33"]

const totalTime = times.reduce((time, nextTime) => {
  return moment(time, "hh:mm")
          .add(nextTime, "hh:mm")
          .format("hh:mm");
}, "00:00");

console.log("total time -->", totalTime);

// total time --> "04:48"

If we added logging inside reduce() to view the accumulation of values:

"12:30"
"02:15"
"04:48"
"total time -->" "04:48"

Notice that the result after the first pass was "12:30". If all times in the array summed to less than one clock hour the end result may not be acceptable for your particular use case.

This worked for me, this function timer is taking 2 times hh:mm:ss and splits it, divides, and then adds them together and after, it formats it to hh:mm:ss again

function timer(tempo1, tempo2) {
  var array1 = tempo1.split(":");

  var tempo_seg1 =
    parseInt(array1[0]) * 3600 + parseInt(array1[1]) * 60 + parseInt(array1[2]);

  var array2 = tempo2.split(":");

  var tempo_seg2 =
    parseInt(array2[0]) * 3600 + parseInt(array2[1]) * 60 + parseInt(array2[2]);

  var tempofinal = parseInt(tempo_seg1) + parseInt(tempo_seg2);

  var hours = Math.floor(tempofinal / (60 * 60));

  var divisorMinutes = tempofinal % (60 * 60);

  var minutes = Math.floor(divisorMinutes / 60);

  var divisorSeconds = divisorMinutes % 60;

  var seconds = Math.ceil(divisorSeconds);

  var counter = "";

  if (hours < 10) {
    counter = "0" + hours + ":";
  } else {
    counter = hours + ":";
  }

  if (minutes < 10) {
    counter += "0" + minutes + ":";
  } else {
    counter += minutes + ":";
  }

  if (seconds < 10) {
    counter += "0" + seconds;
  } else {
    counter += seconds;
  }

  return counter;
}

export default timer;

and on my React App I used this code to keep track of the times and add them calling the timer function

const updateTime = () => {
    let times = [];
    let times2 = [];
    if (todos.length > 1) {
      for (let i = 0; i < todos.length; i++) {
        times.push(todos[i].time + ":00");
      }
      times2 = times[0];
      for (let i = 1; i < times.length; i++) {
        times2 = timer(times2, times[i]);
      }
      times2 = times2.substr(0, 5);
    } else if (todos.length == 1) times2 = todos[0].time;
    else times2 = "No tasks";
    return times2;
  };

I only wanted hh:mm but for the sake of future implementation of seconds if needed, I'm going to add ":00" (seconds) and then remove it again using

times2 = times2.substr(0, 5);