Count Overlapping Minutes from two ranges with multiple criteria

Hi Folks,

I'm trying to calculate the number of minutes in a given month that each particular Aide has been supervised by a BCBA.
Counting the overlapping minutes is what's the tough part- have been at it for a few hrs.

Data fields
1. Employee type (BCBA, Aide)
2. Client
3. Day
4. Time range

Each line is a transaction. Any time a specific Aide is providing service to a specific client at the same time that any BCBA is also providing service to the same client on the same day & time is a supervised minute.

I understand how to group by criteria using sumproduct but I can't figure out how to count the minutes. Please advise