JSFiddle - React, Tailwind, and code Playground
HTML
<input type="text" id="appt_start"/>
<input type="text" id="appt_end"/>
JavaScript
var hash="10:00";
$('#appt_start').val(hash);
var d = new Date("October 13, 1975 "+hash)
d.setMinutes(d.getMinutes()+15);
$('#appt_end').val(d.getHours()+":"+d.getMinutes());