How much do you really work?

I don't mean how many hours are you at work, but how many productive hours do you have a day? Over the last few weeks (we haven't been busy) so I started to think about this at work. I get to work around 9:30 and usually leave about 5:30, which sounds like an 8 hour day, but it is really only 3-4 hours of production. A day in the business world (for those of you in academia) goes like this.
9:30-10 - Read emails and drink coffee
10-11 - Errant meeting that goes over by 30 minutes
11:30-12 - Don't want to start doing anything because I'll be interrupted by lunch
12-1 Lunch
1-1:15 - Digest, read the paper and have another coffee (or other hot caffeinated beverage)
1:15-2:30 - Respond to emails and get some real work done
2:30-3:30 - Errant meeting.
3:30-5:15 - Do work
5:15 - 5:30 - Shut down computer

Say we count the meetings as productive work ... then we get a total of about 5 hours. If we ignore the meetings we get around 3 hours. Again, this is just a sample day. Most of my days, I have many more than 2 meetings, so you can imagine how the productivity decreases.

Now my question is, what if I wasn't required to be there 40 hours a week, and could only show up say 20 hours a week. Would I get as much done? or do I need the 20 hours of reading the paper at work to do the 20 hours of real work?