Naive Timespan class (doesn't account for multiple days)

timespan.js

function Timespan (start, end) {
  /*
   * Todo - handle multiday timespans
   */

  // Make sure times are valid times
  if (!Time.isValid(start) || !Time.isValid(end)) throw new Error('Invalid start or end times');
  // Normalize format ex.'02:15 PM'
  this.start = new Time(start).format('hh:mm AM');
  this.end = new Time(end).format('hh:mm AM')

  var self = this;

  var convertToDateTime = function (time) {
    // Assuming this format ex.'02:15 PM' for time
    var hour = parseInt(time.substring(0, time.indexOf(':'))),
      minutes = parseInt(time.substring(time.indexOf(':')+1, time.indexOf(' ')));
    // Handle PM
    var period = time.substring(time.indexOf(' ') + 1, time.length);
    if (period === 'PM') hour += 12;

    return new Date('2014','10','24', hour.toString(), minutes.toString()).getTime();
  }

  this.overlaps = function (timespanB) {
    // Convert times to Date() times
    var startA = convertToDateTime(self.start),
      endA = convertToDateTime(self.end),
      startB = convertToDateTime(timespanB.start),
      endB = convertToDateTime(timespanB.end);

    if (startA >= endB) return false; // A range completely after B
    else if (endA <= startB) return false; // A range completely before B
    else return true; // Overlap
  }
}

var ts1 = new Timespan('8pm', '8:50pm'),
  ts2 = new Timespan('8pm', '10:50pm');

console.log('Overlap?: ' + ts1.overlaps(ts2));

Requires https://github.com/zever/time