Speed, distance and time

What speed really means

Speed tells you how much ground something covers in a chunk of time. Nothing more complicated than that.

When a car travels 60 kilometres in one hour, we say its speed is 60 kilometres per hour, and write it 60 km/h. The word "per" is doing the work: it means "in every one".

So 60 km/h means 60 kilometres in every one hour. A snail at 3 centimetres per minute covers 3 centimetres in every one minute. Same idea, smaller numbers.

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Three numbers that hold hands

Distance, speed and time always come as a set of three. If you know two of them, the third is already decided — you just have to work it out.

The triangle below is a way of remembering how. Put your thumb over the one you want to find, and what is left is the sum you do.

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Going forwards: how far did it get?

If you know the speed and the time, you can find the distance by multiplying.

Think of it as hops. A car going 60 km/h covers 60 km in the first hour, then another 60 km in the second hour. Two hops of 60 makes 120 km.

That is exactly what 60 × 2 does, which is why distance = speed × time.

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Average speed: one number for the whole trip

Real journeys are not steady. You ride fast downhill and slowly uphill. So we ask a different question: if the whole trip had been at one steady speed, what speed would that have been?

That is the average speed, and there is one rule for finding it. Add up all the distance. Add up all the time. Then divide, once.

Here is a ride in two parts. Thirty kilometres downhill takes an hour. Thirty kilometres back uphill takes two hours.

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The trap almost everyone falls into

The downhill part was 30 km/h. The uphill part was 15 km/h. It is very tempting to add those two speeds and halve them.

Do not. Averaging the two speeds only works if both parts took the same amount of time — and here the uphill part took twice as long.

Because the rider spent more of the trip going slowly, the true average has to be pulled down closer to the slow speed. It is 20 km/h, not 22.5 km/h.

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Keep your units in step

The units in the question tell you the units in the answer. Kilometres and hours give you km/h. Metres and seconds give you m/s.

The one rule is that the two must match before you divide. If a distance is in metres but the time is in minutes, your answer is in metres per minute — which is fine, as long as you say so.

Trouble only starts when you mix them without noticing. Eight hundred metres in half an hour is 800 metres in 30 minutes, so that is about 27 metres per minute. If you want it per hour instead, the time has to be in hours: 800 ÷ 0.5 = 1600 metres per hour. Same journey, two different units, and neither of them is 800 ÷ 30 called "per hour".

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One triangle holds all three sums

Distance sits on top. Speed and time sit underneath, side by side.

Cover the letter you are looking for and the triangle shows you the sum. Cover D and you are left with S next to T, so you multiply. Cover S and D sits above T, so you divide. Cover T and it is D divided by S.

Draw it in the margin before you start. It takes four seconds and removes the commonest error in the topic, which is dividing the right two numbers the wrong way round.

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Sense-check the answer

Every answer here should be believable in the real world. A person walking at 300 km/h has not been calculated, they have been mistyped.

Rough limits worth carrying: a person walks about 5 km/h, runs about 10, a bicycle does 15 to 25, a car on a highway about 100, a train up to about 150.

If your number is wildly outside the range for the thing being described, go back to the triangle before you go back to the arithmetic. It is nearly always the wrong operation rather than the wrong sum.

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