So if I read this correctly, you want to figure out the time that elapsed between start_hour, start_min, end_hour, and end_min, and then store it back in your db

I think I can safely say that it's impossible to detemine ( correctly ) the amount of time that has elapsed by just knowing the hour and minutes, as RheTbull says.

You would need to have some sort of date/time entries for start time and end time, then I think Postgres provides you with ways to calculate an interval type.