PSLE Mathematics Learning Guide · Guide 13
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Speed problems are not three unrelated formulas. They are one relationship viewed from three directions.
Speed = distance ÷ time.
If the speed and time are known, distance can be rebuilt: distance = speed × time. If the distance and speed are known, time can be rebuilt: time = distance ÷ speed.
The difficulty in PSLE-style speed questions usually comes from somewhere else: the units do not agree, the journey has more than one segment, a stop has been included or excluded incorrectly, or the learner averages two speeds instead of using total distance divided by total time.
This guide uses one working habit: identify the journey state, make distance and time units compatible, calculate the relationship, and check the answer against the whole journey rather than one segment.
The MOE Primary Mathematics syllabus updated October 2025 includes speed within Primary Mathematics. The SEAB 2026 PSLE examination-format page links the current Mathematics syllabus. All examples below are original eduKate teaching material.
Start from the meaning of speed
A speed of 60 km/h means 60 kilometres are covered in one hour under the simplified constant-speed model.
At 60 km/h for 2 hours, distance = 60 × 2 = 120 km.
For 120 km travelled in 2 hours, speed = 120 ÷ 2 = 60 km/h.
For 120 km travelled at 60 km/h, time = 120 ÷ 60 = 2 hours.
The three equations are not separate facts. They describe the same journey relationship.
Units must agree before the relationship can be used
If speed is given in km/h, time must be expressed in hours before multiplying directly.
A car travels at 72 km/h for 25 minutes. Convert 25 minutes = 25/60 hour = 5/12 hour.
Distance = 72 × 5/12 = 30 km.
The calculation 72 × 25 treats 25 as hours and breaks the rate unit.
For more detailed conversion practice, use Guide 2: Make Units Agree Before You Calculate.
A journey with several segments needs a journey table
Suppose a cyclist travels 12 km at 12 km/h, then 18 km at 18 km/h.
First segment time = 12 ÷ 12 = 1 hour.
Second segment time = 18 ÷ 18 = 1 hour.
Total distance = 30 km. Total travelling time = 2 hours. Average speed over the moving journey = 30 ÷ 2 = 15 km/h.
A short table prevents segment values from being mixed:
| Segment | Distance | Speed | Time |
|---|---|---|---|
| 1 | 12 km | 12 km/h | 1 h |
| 2 | 18 km | 18 km/h | 1 h |
Average speed is total distance ÷ total time
Average speed is not usually found by adding two speeds and dividing by two.
Example: A runner covers 6 km at 6 km/h and then 6 km at 12 km/h.
First time = 6 ÷ 6 = 1 h.
Second time = 6 ÷ 12 = 0.5 h.
Total distance = 12 km. Total time = 1.5 h.
Average speed = 12 ÷ 1.5 = 8 km/h.
The arithmetic mean of 6 and 12 is 9, which is wrong here because the runner spent different amounts of time at the two speeds.
Decide whether stopping time belongs in the total time
A bus travels 90 km in 1.5 hours and stops for 30 minutes before travelling another 60 km in 1 hour.
If the question asks for average speed while moving, use moving time only: total distance 150 km, moving time 2.5 h, average moving speed = 60 km/h.
If the question asks for average speed for the entire journey from departure to final arrival, include the 0.5-hour stop: total elapsed time = 3 h, average speed = 50 km/h.
The correct denominator depends on what the question means by the journey interval.
Equal distances at different speeds do not give equal times
If the same 60 km is travelled at 30 km/h and then at 60 km/h, the first segment takes 2 hours and the second takes 1 hour.
The slower segment occupies more time and therefore has more influence on the average speed over the combined journey.
Equal times make a different structure
If a vehicle travels for 1 hour at 40 km/h and 1 hour at 60 km/h, the distances are 40 km and 60 km. Total distance = 100 km over 2 hours, so average speed = 50 km/h.
Here the average happens to equal the arithmetic mean because the time weights are equal.
Main worked workshop: fourteen original speed problems
1. Direct speed
150 km in 3 h.
Answer: 50 km/h.
2. Direct distance
45 km/h for 4 h.
Answer: 180 km.
3. Direct time
210 km at 70 km/h.
Answer: 3 h.
4. Convert minutes
60 km/h for 45 min.
Answer: 45 km.
5. Convert seconds
5 m/s for 40 s.
Answer: 200 m.
6. Two segments
30 km in 0.5 h, then 40 km in 1 h. Find average speed.
Answer: 70 ÷ 1.5 = 46 2/3 km/h.
7. Equal distance, different speed
40 km at 20 km/h, then 40 km at 40 km/h.
Reasoning: Times 2 h and 1 h. Average = 80 ÷ 3 = 26 2/3 km/h.
8. Equal time, different speed
2 h at 30 km/h and 2 h at 50 km/h.
Answer: total distance 160 km over 4 h = 40 km/h.
9. Stop included
A van travels 120 km in 2 h, stops 30 min, then travels 60 km in 1 h. Average from departure to arrival?
Answer: 180 ÷ 3.5 = 51 3/7 km/h.
10. Stop excluded
Same journey, average while moving?
Answer: 180 ÷ 3 = 60 km/h.
11. Find missing segment speed
A 100-km journey takes 2 h. First 40 km takes 1 h. Remaining 60 km takes 1 h. Find second speed.
Answer: 60 km/h.
12. Find missing time from total journey
A journey totals 180 km. First 60 km takes 1 h. Remaining 120 km is travelled at 60 km/h.
Answer: remaining time 2 h; total 3 h.
13. Compare two routes
Route A: 90 km in 1.5 h. Route B: 120 km in 2 h.
Answer: both average 60 km/h.
14. Reject averaging speeds
10 km at 10 km/h and 10 km at 20 km/h. A learner says average = 15 km/h.
Repair: Times are 1 h and 0.5 h. Average = 20 ÷ 1.5 = 13 1/3 km/h.
A journey-control table
| Question | Relationship | Main check |
|---|---|---|
| Find speed | distance ÷ time | units become distance per time |
| Find distance | speed × time | time unit matches speed denominator |
| Find time | distance ÷ speed | answer unit matches time |
| Average speed | total distance ÷ total relevant time | all segments included correctly |
Use distance–time thinking even without a graph
A distance–time story can be read as changes in distance over elapsed time. If distance does not change while time passes, the traveller is stationary. If more distance is covered in the same amount of time, the speed is greater.
This interpretation helps learners connect tables, word problems and later graph work without needing to memorise disconnected formats.
Common speed errors
Error 1: Use minutes directly with km/h.
Error 2: Average segment speeds instead of total distance ÷ total time.
Error 3: Include a stop when the question asks for moving speed, or exclude it when the question asks for total journey average.
Error 4: Find an intermediate segment distance and report it as the whole journey distance.
Error 5: Change units in one quantity but not the other.
Independent transfer check
- 84 km in 1.5 h. Find speed.
- 72 km/h for 35 min. Find distance.
- 96 km at 48 km/h. Find time.
- 20 km at 20 km/h, then 30 km at 30 km/h. Find average speed.
- A journey has 2 h moving time and a 30-min stop. Total distance is 100 km. Find the whole-journey average speed.
- For the same journey, find average moving speed.
- Explain why averaging 20 km/h and 40 km/h may not give the true journey average.
- Explain what information decides whether stopping time belongs in the denominator.
Independent-check answers
1. 56 km/h.
2. 35 min = 7/12 h; distance = 42 km.
3. 2 h.
4. Each segment takes 1 h, so total 50 km over 2 h = 25 km/h.
5. 100 ÷ 2.5 = 40 km/h.
6. 100 ÷ 2 = 50 km/h.
7. The two speeds may apply for different distances or times, so they may carry different weights in the whole journey.
8. The wording defining the journey interval: moving time only or total elapsed time from departure to arrival.
Parent and tutor guide
Ask the learner to draw a four-column table: segment, distance, speed, time. Do not supply the formula first. Ask which two quantities are known in each row.
If the child averages speeds directly, ask for total distance and total time. If stopping time is mishandled, underline the exact wording that defines the journey interval.
After a correct solution, change one unit or insert a stop. This tests whether the relationship survives a surface change.
The learner’s final card
Which journey segment am I working on? Do the distance and time units agree with the speed unit? What is the total distance? What time interval does the question actually mean? For average speed, did I divide total distance by total relevant time?
Continue through the PSLE Mathematics Learning Guide
Continue with Guide 14: Use Factors and Multiples to See Grouping and Repetition, Guide 15: Read the Order of Operations Before You Calculate, and Guide 16: Round and Estimate Without Replacing the Exact Question.
Return to the PSLE Learning Guide.
Sources and boundaries
Official references: SEAB 2026 PSLE formats and MOE Primary Mathematics syllabus, updated October 2025.
Teaching boundary: All examples and suggested solutions are original eduKate teaching material. Simplified constant-speed models are used where stated.