Calculating Duration Of Activities Per Hour

My data is in the following form:

CREATE TABLE Temp (ORG_NAME VARCHAR(20), START_TIME datetime, END_TIME datetime)

INSERT INTO Temp VALUES('Org Name', '2014-06-20 14:25:00.000', '2014-06-20 15:25:00.000') - AND many more like these with different START_TIME and END_TIME.

The Task:

- I need to calculate the duration of the activities PER HOUR.

i.e. in the example above, if I want to see the productivity for 2PM (i.e. activity duration from 2-3PM), I should only get 35 mins (as the activity started at 14:25). In the same way, if I see the productivity for 3PM (i.e activity duration from 3-4 PM), I should only see 25 minutes (as activity ended at 15:25).

There would technically be many activities with overlapping times - for example, there might be 5 activities starting at 14:30 and ending at 15:10. In this case, if I were to see the productivity for 2PM, I'd see 150 minutes (as each activity starts at 14:30, so 30 min per activity = 150 min). In the same way, if I saw the productivity for 3PM for those 5 activities, I'd see 50 minutes.