Calculate speeds and average a whole journey
Use distance = speed × time with matching units · Convert between common speed units · Average using total distance and total elapsed time
Section Paper 1 · Historical Core · non-calculator
Exam scope and assessment notes
Core and Extended foundations. Historical study of Cambridge IGCSE Mathematics (US) 0444, 2025 Version 2. The final assessment was June 2025; the syllabus was available only to schools in Arizona, USA. This is not a current exam-entry option. Original self-check teaching and explained practice are not Cambridge papers, official marks or predicted grades. Linked teaching foundations do not establish full syllabus mastery. Calibrated cumulative assessment, reliable drawn-work review and qualified mathematics-teacher review remain unfinished.
Before you begin
- Time conversions
- Ratios and units
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What should you establish before applying the method in this lesson?
What you will learn
- Use distance = speed × time with matching units
- Convert between common speed units
- Average using total distance and total elapsed time
Match the units
s = d/t for positive duration, d = st, and t = d/s for positive speed. Kilometres per hour require hours; metres per second require seconds. Multiply m/s by 3.6 to get km/h, and divide km/h by 3.6 for m/s.
Average over the stated journey
Average speed is total distance divided by total elapsed time, including stops if they lie within the requested journey. It is not generally the arithmetic mean of segment speeds. Distance is the path length, not a signed displacement.
For equal distances at different speeds, segment times differ. Add the actual durations before calculating the overall average; check what start and end times the question includes.
Sources for this lesson
Pause and explain
How is average speed calculated for a journey?
Worked example
Travel 60 km at 30 km/h, then 60 km at 60 km/h. Find the average speed.
Show the worked solution
- The segment times are 2 hours and 1 hour.
- Total distance 120 km divided by total time 3 hours gives 40 km/h.
Answer 40 km/h, not the arithmetic mean 45 km/h.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Travel 24 km in 30 minutes. Find the average speed in km/h.
Give me a hint
Convert 30 minutes to hours.
Compare my reasoning
- 30 minutes = 0.5 hour.
- 24/0.5 = 48 km/h.
48 km/h.
Look for these in your work
- Match time units
- Check the result's scale
Convert 72 km/h to m/s, then find the distance travelled in 15 seconds at that constant speed.
Give me a hint
Divide by 3.6 before using seconds.
Compare my reasoning
- 72/3.6 = 20 m/s.
- 20×15 = 300 m.
20 m/s; 300 m.
Look for these in your work
- Convert the speed
- Use constant-speed assumptions
A cyclist covers 12 km in 40 minutes, rests 20 minutes, then covers 18 km in 60 minutes. Find average speed from departure to arrival.
Give me a hint
Include the stop in elapsed time.
Compare my reasoning
- Distance = 30 km; elapsed time = 120 minutes = 2 hours.
- 30/2 = 15 km/h.
15 km/h including the rest.
Look for these in your work
- Sum distances and durations separately
- Use the stated journey endpoints
Common mistakes
- Convert minutes to hours before using km/h.
- Do not average speeds without checking their time weights.
What can you explain now?
How is average speed calculated for a journey?
Compare with the explanation
Total distance divided by total elapsed time.
Every included segment and stop contributes to the journey totals.
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Make it stick
How is average speed calculated for a journey?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.