Every driver has lived it: a journey planned at motorway speed that arrives an hour late, despite long stretches at 110 km/h and no visible disaster. Nothing went wrong — the plan was wrong, in a specific mathematical way that afflicts every mixed-speed journey. This article explains why averages over distance behave so counterintuitively, works the classic example, and gives an estimation method whose arrival times survive contact with real roads.
The illusion has a mirror image worth knowing: on journeys that are almost entirely fast road, drivers underestimate how good their average can be — and then schedule arrivals they beat by embarrassing margins, to the delight of nobody waiting. The arithmetic is impartial; it humbles both directions of guess.
Time is added per kilometre, not per hour
The root of the illusion: a journey’s time is the sum of distance-over-speed for each part, and slow parts contribute disproportionately. Cover 20 km of town at 30 km/h and it costs 40 minutes — as much time as 73 km of motorway at 110. Drivers intuitively average speeds; journeys actually average slowness. The correct overall average is the harmonic mean over distance, and it always lands nearer the slowest section than intuition expects. A trip that is 80% motorway by distance is nothing like 80% motorway by time.
Key takeaways
- Slow kilometres cost time out of all proportion to their length
- True average speed ≈ total distance ÷ total time, always lower than the cruise
- A 180 km mixed trip planned at ‘110’ honestly averages 65–75
| Leg | Distance | Speed | Time |
|---|---|---|---|
| Motorway | 140 km | 110 km/h | 1 h 16 min |
| Country roads | 25 km | 60 km/h | 25 min |
| Town at each end | 15 km | 30 km/h | 30 min |
| Whole trip | 180 km | — | 2 h 11 min (avg 82) |
Why sat-navs seem pessimistic (and are right)
Navigation systems learned this arithmetic from billions of journeys, which is why their estimates initially feel insulting and usually prove accurate. They model each segment at its observed speed distribution — including the lights, the roundabout queue, the school zone at 8:40 — and sum times, not speeds. When your estimate disagrees with the machine’s, the disagreement is almost always your average-speed assumption, not its pessimism. Our travel time calculator asks for a realistic average and warns about exactly this; the honest way to get that number is from your own previous similar trips, where your sat-nav history holds it precisely.
Why the last ten kilometres feel endless
Every journey’s slowest segment is usually its last: the destination town, the search for the street, the car park. Psychologically it expands because attention, freed from the motorway’s trance, starts counting minutes again — but the mathematics is real: those final kilometres at 20 km/h cost three minutes each, the price of nine motorway kilometres. Route planners who budget the last stretch as its own segment, at walking-adjacent speeds, stop being surprised by it. Our travel time calculator’s break allowance gestures at this; the full discipline is to segment the journey honestly all the way to the door, including the door.
Delivery drivers and couriers — the professionals of arrival — plan exactly this way instinctively: their mental map prices the destination neighbourhood, not just the road to it. The last mile is a place, not a rounding error.
Trains, planes and the door-to-door honesty test
The same arithmetic judges every mode comparison you will ever make. The flight is one hour; the journey is five — two ends of ground travel, security, boarding, the wait designed into airports. The train’s headline time is station to station; yours is door to door. Driving’s great competitive advantage is that its door-to-door average is the number this article teaches you to compute, with no transfers hiding inside. Whenever a mode advertises a speed, ask for its door-to-door time on your actual journey; the illusion this article describes is the marketing department of every fast thing, quietly averaging only the fast part.
Apply the segments test and the modes often reorder themselves — the ‘slow’ train through the city centre beats the ‘fast’ flight to its outskirts with suspicious regularity.
Freight, buses and the professional version
The illusion scales up into the economics of everything that moves. Haulage firms price routes by time-segment models, not distances, because a 400 km route through two cities can cost more driver-hours than a 550 km route around them; bus timetables are built from segment running times learned the hard way; and the logistics industry’s central discovery of the last half-century is that reliability — the variance of the average — matters more to customers than the average itself. Your family journey obeys the same laws at one-thousandth the scale: the arrival estimate that matters is the pessimistic-but-typical one, the journey you will actually have on an ordinary day, not the record run of a clear Sunday dawn.
Plan to the typical, celebrate beating it, and the road stops being a casino. That is the entire article in one sentence; everything else was arithmetic.
One last calibration: your own last journey
Before your next long drive, try the experiment this article has been quietly prescribing: write down your predicted arrival before you leave, using the segment method, and compare it with the door-to-door truth when you arrive. Most people’s first attempt is still optimistic — the ends of the journey are slower than even a warned planner admits — but the second attempt is usually within ten minutes, and the third is boringly accurate. That is the whole skill: not a formula, but a calibrated intuition with the arithmetic installed underneath it.
Planning that survives reality
Three habits fix arrival estimates. Use segment thinking: split the journey into fast, medium and slow parts and price each in time, even roughly. Anchor on the door-to-door average from a previous similar journey — one data point of your own beats a page of theory. And pad the ends: the first and last fifteen minutes of any trip are reliably slower than the plan admits — leaving is a process, arriving involves parking, and neither appears in distance ÷ speed at all. The break allowance matters too: six minutes per hour is the floor on long drives, and it belongs in the arrival time, not in a footnote.
Common mistakes
- Estimating with the fastest speed of the trip
- Treating the sat-nav’s estimate as pessimism to be beaten
- Forgetting that stops, fuel and traffic are part of the journey, not interruptions to it
Questions this raises
For a motorway-heavy mix, 75–85 km/h door-to-door is a realistic planning band; for country-road routes, 55–65; for urban, 25–35. Your own history beats every band.
Barely — raising motorway pace from 110 to 130 in the example saves about ten minutes while raising fuel use by a fifth. The slow segments own your arrival time.
Put a number on it.
You cruised at 110. You averaged 68. The arithmetic of mixed-speed journeys, and how to estimate arrival times that survive contact with reality.
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