When I originally wrote this I used to live 15 miles from work and it took me 30 minutes to drive it. Enter 15 for distance, enter 30 for time, and press the calculate button next to speed (the value I want to solve for). My average speed appears as 30 mph even though most of my trip is at the speed limit of 55 mph. So the traffic lights and other traffic shoot my average to hell.
To adjust for the traffic lights, check the box and enter how many lights you drive through and how many seconds to allot per light. I go through 24 traffic lights and have decided on making 20 seconds the default, so I'll try that. This gives me an average speed of 41 mph, which is probably realistic seeing that some segments are at 30 mph and others are at 35 mph.
You may want to play with these figures until you find amounts that work for your driving style. Then you can get more accurate data.
In order to shave 5 minutes off of my travel time; using the above data, enter 25 for minutes and press calculate next to speed. We get 53 mph (52.9 to be exact, if you try the formula via a calculator). So I would need to increase my average speed 12 mph over the entire route in order to compensate for the traffic lights and other traffic along my route. Seeing that most police officers grab people in excess of 5 mph over the speed limit (higher being a sweeter target), this puts us right in their sights.
The moral of this story: If you are going to be late, just accept it. Unless your trip is over a very long distance you won't really gain much. You'll have to leave earlier to get there on time. So, why do people speed? Probably because they haven't done the math, or maybe they just like going fast. You tell me.