Travel time:
why distance ÷ speed is only the start

The core relationship between distance, speed and time

Three quantities describe a journey, and any one can be found from the other two. Speed is distance covered per unit of time. Rearranged, time is the distance divided by the speed.

The result is in hours because the speed was per hour. If your speed is in metres per second and the distance in kilometres, convert one of them first, or the answer will be off by a factor of 1,000.

The relationship rearranges in two other ways, which is useful when a trip has a deadline. The speed you need is distance divided by the time available, and the distance you can cover is speed multiplied by time. If you must travel 180 km in 2.5 hours, the required average is 72 km/h, and whether that is realistic depends on the road.

Turning decimal hours into hours and minutes

A common slip is reading a decimal as minutes. A result of 2.75 hours is not 2 hours 75 minutes. The part after the decimal point is a fraction of an hour, so multiply it by 60.

Look at the shape of the table. Moving from 40 to 50 km/h saves 54 minutes, while moving from 70 to 80 km/h saves only 19. Each extra kilometre per hour buys less time as speeds rise, which is a good reason to be sceptical of the value of speeding.

Another conversion catches people out when speeds are in mph and distances in kilometres, or the reverse. Convert the distance or the speed first, using 1 mile ≈ 1.609 km, and only then divide. Mixing the two without conversion is the single biggest cause of wrong estimates on holiday road trips abroad.

The average-speed trap on mixed roads

Real trips are not at one speed. A highway section, a town stretch and a ghat road each have their own pace. The speed you use in the formula has to be the average over the whole distance, weighted by time, and it is not the simple mean of the speeds on each leg.

Take a 200 km round trip, 100 km each way. You drive out at 50 km/h and return at 100 km/h. The simple mean is 75 km/h, but the legs take 2 hours and 1 hour, so 200 km takes 3 hours and the true average is about 66.7 km/h.

The cleaner method is to compute time on each leg and add. A trip with 60 km at 40 km/h and 120 km at 80 km/h takes 1.5 + 1.5 = 3 hours, which gives an average of 180 ÷ 3 = 60 km/h. The answer matches the plain mean of 40 and 80 only because the two legs took the same 1.5 hours each. Change the lengths of the legs and the two methods part company.

From driving time to arrival time

Driving time is only a part of the elapsed time. For an arrival estimate, add whatever the trip actually contains and subtract nothing optimistic.

• Rest stops: a short break every two hours or so is a common planning figure, and children or older passengers often need more.
• Fuel and charging stops, which depend on tank or battery range.
• Toll plazas, level crossings and city entry points that slow traffic.
• Time of day: peak-hour traffic can cut the average speed by a third or more on the same road.
• Weather and road works, which are worth checking on the day.

A reasonable habit is to build the estimate in two parts. Take the pure driving time from the formula, then add a separate allowance for stops and traffic, and give the passengers both numbers. If the drive is 3 hours and you allow two 15-minute stops, plan for 3 h 30 min.

Planning with a buffer and a margin of error

The right estimate depends on what happens when you are late. A weekend drive to a hill station has a forgiving schedule. A road journey to catch a flight does not. For the second case, plan from the pessimistic end, using a lower average speed and extra stops.

One approach is to compute two times. The optimistic time uses the best realistic average, for instance 70 km/h on a clear highway. The cautious time uses a weaker figure, such as 50 km/h. For 180 km these are 2 h 34 min and 3 h 36 min, a gap of over an hour. Showing both to everyone involved is more honest than quoting one number and then explaining the miss.

A buffer of 15 to 20 per cent on the cautious time is a common allowance for hard deadlines, although the right amount depends on route, season and time of day. Reviewing the actual time against your estimate after each trip improves the next one more than any extra formula.

When the estimate lets you down

The formula is exact for a constant average speed and an exact distance. Routes are rarely either. Navigation apps use live traffic, but they also predict, and predictions miss on the occasional day with an accident or a diversion.

Posted speed limits make a poor average. They are a ceiling for good conditions, and your overall pace is lower once junctions, queues and overtaking are included. For long routes, use your own recorded average from earlier trips on the same road, or a figure from a navigation app, in preference to the limit.