60 km/h out, 30 km/h back: is the average speed 45 km/h?

On the left are the one-way distance and the speeds out and back. On the right, from the top: total distance, average speed and total time. The average speed divides the total distance above it by the total time below it. The bottom card simply averages the two speeds.

Why not 45?

Average 60 and 30 directly and you get (60 + 30) ÷ 2 = 45. The board's Mean of the two speeds shows 45 km/h too.

But average speed is total distance ÷ total time. Averaging the speeds on their own does not give it.

1 hour out, 2 hours back

The distance is 60 km both ways, but the time is not.

This board splits the total time into the trip out and the trip back.

• Out, at 60 km/h — 60 ÷ 60 = 1 hour
• Back, at 30 km/h — 60 ÷ 30 = 2 hours

The way back takes twice as long. That is why the slower 30 km/h counts for more in the round trip as a whole.

Look at the whole round trip

• Total distance — 60 × 2 = 120 km
• Total time — 1 + 2 = 3 hours
• Average speed — 120 ÷ 3 = 40 km/h

The first board's Average speed is exactly this division: total distance ÷ total time.

Try it yourself

Keep 60 km each way and change the speeds out and back.

When the two speeds are the same, the two numbers agree. The further apart the speeds, the more the average speed leans towards the slower one, because that is the leg you spend longer on.

When the same distance is covered at two speeds, the average speed can also be written as 2 × speed out × speed back ÷ (speed out + speed back). That form is called the harmonic mean. For 60 and 30: 2 × 60 × 30 ÷ 90 = 40.

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