A 100 kilometre trip takes 60 minutes at 100 km/h. At 110 km/h it takes 55 minutes. The whole reward for travelling ten per cent faster for an hour is five minutes.
Push to 120 km/h and the trip takes 50 minutes. Two full increments of ten kilometres per hour, sustained the entire way, bought ten minutes.
The relationship is upside down
Time is distance divided by speed, so speed sits in the denominator. Equal steps in speed do not produce equal steps in time, and each additional increment saves less than the one before it.
Over the same 100 kilometres:
- 80 km/h: 75 minutes
- 90 km/h: about 67 minutes, saving 8
- 100 km/h: 60 minutes, saving 7
- 110 km/h: 55 minutes, saving 5
- 120 km/h: 50 minutes, saving 5
The first ten kilometres per hour saved eight minutes. The last saved five. This is the same reciprocal effect that makes miles per gallon misleading, covered in the piece on fuel economy: when the quantity you care about is the reciprocal of the one you are changing, equal steps stop being equal.
Short trips are where it disappears entirely
Most driving is not 100 kilometres. On a 10 kilometre trip, the whole gap between 50 km/h and 60 km/h is two minutes. On a 5 kilometre run to the shops it is one.
That is the honest scale of what aggressive driving buys on the trips people actually make, and it is before a single red light, roundabout or give-way sign has been counted.
Average speed is not the speed you drive
The figures above assume the higher speed is held for the entire distance. In practice it never is. Traffic, lights and turns set the average, and on an urban trip those dominate so completely that the top speed reached between them barely moves the total.
This is why a trip that felt fast and a trip that felt slow so often take the same time. The speed, distance and time calculator works in average speed, which is the figure that determines arrival time, and the average speed calculator works it out from a trip you have already made.
The costs go the other way
Fuel consumption rises with speed, and it rises faster than speed does, because air resistance grows with the square of velocity. So the trip that saves five minutes also burns more fuel, and the fuel cost per kilometre calculator will price that if you enter the higher consumption figure your car actually returns at that speed.
None of this is an argument about road rules, which are set on safety grounds rather than arithmetic ones. It is simply that the time being bought is usually smaller than it feels, and on a short trip it is close to nothing.