If you want to use both date and time picker at the same time, the simple and easy way is to use jquery UI timepicker add-on, it works with exisitng jquery datepicker.
solution
<script src="jquery.min.js"></script>
<script src="jquery-ui.min.js"></script>
<script src="jquery-ui-timepicker-addon.js"></script>
After that call it
<script type="text/javascript">
$(document).ready(function () {
$("#date").datetimepicker({
dateFormat: 'dd-mm-yy', timeFormat: 'hh:mm:ss'
});
});
</script>
@Html.TextBoxFor(m => m.StartTime, new {id = "date"})