If you want the simplest way, just use JavaScript in your Twine code. For example:
<<script>>State.variables.CurDate = new Date('August 19, 1975 23:15:30');<</script>>
$CurDate
<<script>>State.variables.CurDate = new Date(State.variables.CurDate.getTime() + 15*60000);<</script>>
$CurDate
In the above case it sets $CurDate to "August 19, 1975 23:15:30", displays the date and time as " 8/19/1975, 11:15:30 PM", then adds 15 minutes (60,000 milliseconds = 1 minute), and then it should display "8/19/1975, 11:30:30 PM".
You could make that a JavaScript function if you wanted to make that easier. Just add this to your JavaScript section:
window.addMinutes = function(Min) {
State.variables.CurDate = new Date(State.variables.CurDate.getTime() + Min*60000);
return State.variables.CurDate;
};
Then in your Twine code you'd just do something like "<<set addMinutes(15)>>" or "<<print addMinutes(15)>>, and that would increment the time by 15 minutes, and in the latter case it would also display that new time.
So, just set your start date like above initially somewhere, and then add however much time you want. You can use the various JavaScript Date functions if you'd like to manipulate or set the date and/or time in other ways.
Hope that helps! :-)