calculating a time range into predefined time slots

I have a two columns one with a start time and the other with an end time. These times can be any amount of time during the day and in 24 hour time format for example the start could be 03:43:00 and the end could be 6:13:00. I then have 6 other columns that break the day up into 4 hour time slots for example the first is 0:01-4:00 second 4:01-8:00 and so on. What my objective is to calculate the sum of the hours using only the start and end times and then separate the totals into each time slot. So using the above example of the start 03:43:00 we will say it is A1 and the end 6:13:00 in B1 then 00:17:00 would be in the 0:01-4:00 time slot and 02:13:00 would be in the 4:01-8:00 time slot.

I have a good knowledge of web programming and databases but I just don't know excel forumulas very well. If I can't get this I'm just going to make a database and use a web UI to do my queries but here is an example of what I started doing for the first time slot but I know its way off the mark
=SUM((B1<=TIME(4,0,0))-(A1>=TIME(0,1,0)))

that works well... I understand your logic in the formula and it was a smart thing to subtract the running total from in each new time slot. I may add some rounding to it to the nearest half hour but I think it might be best left rounded by the human eye for the time being. It is for time sheets and in the end the final version needs to be hand written on an official time sheet and this would just be by my personal record but make the process much more easy and error free for me. thanks!