Edit in JSFiddle

var numWritten = {
  "and": 0,
  "a": 1,
  "an": 1,
  "one": 1,
  "two": 2,
  "three": 3,
  "four": 4,
  "five": 5,
  "six": 6,
  "seven": 7,
  "eight": 8,
  "nine": 9,
  "ten": 10,
  "eleven": 11,
  "twelve": 12,
  "thirteen": 13,
  "fourteen": 14,
  "fifteen": 15,
  "sixteen": 16,
  "seventeen": 17,
  "eighteen": 18,
  "nineteen": 19,
  "twenty": 20,
  "thirty": 30,
  "forty": 40,
  "fifty": 50,
  "sixty": 60,
  "seventy": 70,
  "eighty": 80,
  "ninety": 90,
  "hundred": 100,
  "thousand": 1000
};

var unitsFirstLetter = {
  "s": 1,
  "m": 60,
  "h": 3600
};

var testDigits = new RegExp("[0-9]+");
var testUnits = new RegExp("[A-z]+");

function duration(text) {
  var dur = 0;
  var words = relavantWords(text.toLowerCase());
  var units;

  for (var i = 0; i < words.length; i++) {
    // if it's a number & unit
    if (testDigits.test(words[i]) && testUnits.test(words[i])) {
      var n = words[i].match(/[0-9]+/)[0]
      var u = words[i].match(/[A-z]/)[0];

      dur += parseInt(n) * unitsFirstLetter[u];
    }

    // otherwise we're dealing with the unit alone
    else if (testUnits.test(words[i])) {
      var u = unitsFirstLetter[words[i][0]];

      // assemble a number, like [3, 100, 40, 5] into 345
      var numbers = [];
      for (var j = i - 1; j >= 0; j--) {
        numbers.unshift(parseInt(words[j]));

        if (j > 0 && testUnits.test(words[j - 1])) {
          break;
        }
      };
      var n = getNumber(numbers);

      dur += n * u
    }
  };

  return dur;
}

function relavantWords(text) {
  // first check for any numbers written out
  var words = text.replace("-", " ").split(" ");
  for (var i = 0; i < words.length; i++) {
    var keyNum = Object.keys(numWritten).indexOf(words[i]);
    if (keyNum >= 0) {
      words[i] = numWritten[words[i]];
    }
  };

  var relavant = [];
  // go through each word
  for (var i = 0; i < words.length; i++) {
    // if it has a digit, it's definitely relavant
    if (testDigits.test(words[i])) {
      relavant.push(words[i]);
    }
    // to capture units, see if the previous one had numbers and no digits
    else if (testDigits.test(words[i - 1]) && !testUnits.test(words[i - 1])) {
      relavant.push(words[i]);
    }
  };
  return relavant;
}

function getNumber(numbers) {
  if (numbers[0] == 0) {
    numbers[0] = 1;
  } // **exception: if 0 is first, then change it to a 1
  if (numbers.length == 1) {
    return numbers[0];
  } else {
    var twoNums = numbers.splice(0, 2);

    if (twoNums[0] > twoNums[1]) {
      // two numbers and the first one's bigger: add them
      // fifty three, twenty nine
      var s = twoNums[0] + twoNums[1];
      numbers.unshift(s);
      return getNumber(numbers);
    } else {
      // two numbers and the first one's smaller: multiply
      // four hundred = 4 * 100
      var m = twoNums[0] * twoNums[1];
      numbers.unshift(m);
      return getNumber(numbers);
    }
  }
}

function main() {
	var words = document.getElementById('words').value;
	var d = duration(words);
  document.getElementById('duration').innerHTML=d+" seconds"; 
}

  <input id="words" type="text" placeholder="23mins two secs" />
  <button onclick="main()" type="submit">Go</button>
  <div>
    <p id="duration">
    1382 seconds
    </p>
  </div>