From http://www.chroder.com/2014/02/01/using-ngmodelcontroller-with-custom-directives/

TimeDurationDirective.js

function TimeDurationDirective() {
  var tpl = "<div> \
     <input type='text' ng-model='num' size='80' /> \
     <select ng-model='unit'> \
         <option value='secs'>Seconds</option> \
         <option value='mins'>Minutes</option> \
         <option value='hours'>Hours</option> \
         <option value='days'>Days</option> \
     </select> \
 </div>";

  return {
      restrict: 'E',
      template: tpl,
      require: 'ngModel',
      replace: true,
      link: function(scope, iElement, iAttrs, ngModelCtrl) {
          // Units of time
          multiplierMap = {seconds: 1, minutes: 60, hours: 3600, days: 86400};
          multiplierTypes = ['seconds', 'minutes', 'hours', 'days']

          ngModelCtrl.$formatters.push(function(modelValue) {
              var unit = 'minutes', num = 0, i, unitName;

              modelValue = parseInt(modelValue || 0);

              // Figure out the largest unit of time the model value
              // fits into. For example, 3600 is 1 hour, but 1800 is 30 minutes.
              for (i = multiplierTypes.length-1; i >= 0; i--) {
                  unitName = multiplierTypes[i];
                  if (modelValue % multiplierMap[unitName] === 0) {
                      unit = unitName;
                      break;
                  }
              }

              if (modelValue) {
                  num = modelValue / multiplierMap[unit]
              }

              return {
                  unit: unit,
                  num:  num
              };
          });

          ngModelCtrl.$parsers.push(function(viewValue) {
              var unit = viewValue.unit, num = viewValue.num, multiplier;
              multiplier = multiplierMap[unit];
              return num * multiplier;
          });

          scope.$watch('time_unit + time_num', function() {
              ngModelCtrl.$setViewValue({ unit: scope.unit, num: scope.num });
          });

          ngModelCtrl.$render = function() {
              if (!$viewValue) $viewValue = { unit: 'hours', num: 1 };

              scope.unit = ngModelCtrl.$viewValue.unit;
              scope.num  = ngModelCtrl.$viewValue.num;
          };
      }
  };
};