How to find average speed
Average speed is one line of maths. It is also one of the most reliably failed questions in school maths, because the obvious shortcut is wrong.
The formula
Average speed = total distance over total time.
That is it. Note the word total, twice. You add up the whole journey first, and you divide once at the end.
The trap: you cannot average the speeds
Here is the question that catches almost everybody.
A car drives 60 km at 60 km/h, then 60 km at 30 km/h. What is the average speed for the whole trip?
The tempting answer is 45 km/h, the average of 60 and 30. It is wrong.
Do it properly:
- First part: 60 km at 60 km/h takes 1 hour.
- Second part: 60 km at 30 km/h takes 2 hours.
- Total distance: 120 km. Total time: 3 hours.
- Average speed: 120 divided by 3 is 40 km/h.
Forty, not forty-five.
Why? Because the car spent twice as long going slowly. The slow part gets more weight in the average, and averaging the two numbers gives them equal weight.
The rule to remember: averaging the speeds only works when the two parts took the same amount of time. When the two parts cover the same distance, which is the usual exam setup, averaging the speeds is always wrong.
The method that always works
Three steps, in this order:
- Find the time for each part of the journey. Time equals distance divided by speed.
- Add up all the distances. Add up all the times.
- Divide total distance by total time. Once.
Never divide in the middle. Never average anything but the final step.
Units: convert first
Mixed units cause more lost marks than the trap does.
If the speeds are in km per hour, every time must be in hours before you add anything.
- 30 minutes is 0.5 hours.
- 45 minutes is 0.75 hours.
- 90 minutes is 1.5 hours, not 1.3.
- 1 hour 20 minutes is 1 and one third hours, about 1.333.
Minutes are sixtieths, not hundredths. Write the conversion down as its own line so you can see it.
Stops count
If a journey includes a 20 minute stop, that 20 minutes goes into the total time.
Average speed describes the whole journey from start to finish. A train that covers 180 km in 3 hours has an average speed of 60 km/h, even if it stood still at a station for half an hour and hit 120 km/h in between.
Only leave the stop out if the question asks for the average speed while moving, and it will say so.
A worked example with mixed units
A cyclist rides 12 km in 40 minutes, rests for 20 minutes, then rides 18 km in 1 hour. What is the average speed for the whole trip in km/h?
- Total distance: 12 plus 18 is 30 km.
- Total time: 40 minutes plus 20 minutes plus 60 minutes is 120 minutes, which is 2 hours.
- Average speed: 30 divided by 2 is 15 km/h.
The rest went into the total time. If you left it out you would get 18 km/h, which answers a question nobody asked.
Rearranging the formula
The same relationship gives you all three quantities:
- Speed = distance over time
- Distance = speed times time
- Time = distance over speed
A lot of students memorise a triangle diagram for this. That works, but it is quicker to check with units. Kilometres divided by hours gives km/h, so that one must be speed. Km/h times hours leaves kilometres, so that must be distance.
Units are a free check on every rearrangement.
How to practise it
Do five questions where the two parts cover the same distance at different speeds. Write down the two times before anything else.
Then do five where the two parts take the same time at different speeds, and notice that averaging the speeds now does work.
Understanding why one works and the other does not is worth more than twenty mixed questions.
FutureSchool covers speed, distance and time in its Maths programme with a video lesson, a worksheet and a test for each step, so the unit conversion gets practised on its own. It appears in the lower secondary years and again in GCSE revision.
To find out which topics your child has secure, start with the free assessment.
Questions parents ask
What is the formula for average speed?
Average speed equals total distance divided by total time. Add up every part of the journey first, then divide once.
Can I just average the two speeds?
No, unless the two parts took the same amount of time. Averaging speeds is wrong whenever the distances are equal, which is the usual exam setup.
Does average speed include time spent stopped?
Yes. Average speed uses the total time for the whole journey, stops included. Only average the moving time if the question explicitly asks for speed while moving.
How do I handle mixed units?
Convert everything to one pair of units before you divide. 90 minutes is 1.5 hours, not 1.3. Getting that wrong is the most common unit mistake.