PL/SQL :: How To Check If Time Is Closer To Start Or End Time

I have a table which stores apointment start times and appointment end times. For the sake of this thread I will call them appt.start_time and appt.end_time. I then have a check in time and a check out time for the customer. The only thing is they ONLY way to distinguish between a check in time and a check out time is which one has the earlier time and which one has the later time. Obviously the earlier time will be the check and the later time will be the check out.

This is fine, however sometimes they may forget to check a person in or out and I need to determine whether the time should be insert into the check_in column or the check_out column. To do this I was thinking of comparing the time with the appointment start and end time and if it was closer to the appointment start time put it into the check_in column and if its closer to the appointment end time put it into the check_out column. But I was wondering how I would go about doing this.

The time I will want to compare against the appointment start and end time I will store in a variable called v_time and have this as part of my query, im just unsure of what way to write the query so as to check if the time is closer to the start or end time.