PSLE Speed Problems: Catching Up, Meeting and Average Speed

PSLE Speed Problems become much easier when pupils stop treating speed as a single formula and begin reading the movement. Every question lives inside the same relationship: distance = speed × time. Catching-up, meeting, average speed and journey problems differ only in how distance and time are organised.

Students searching for PSLE speed questions, catching-up problems, meeting problems, average speed, speed-distance-time or Primary 6 rate problems often memorise triangles and formulas first. The more reliable method is draw the journey → identify the moving quantities → align units → choose the relationship → solve → return to the story.

This page is the canonical Speed owner under the PSLE Mathematics Heuristics hub. It treats speed as a relationship and representation problem, not a formula-recitation exercise.

Quick answer: the three core relationships

Distance = Speed × Time
Speed = Distance ÷ Time
Time = Distance ÷ Speed

The formula chosen should match the unknown quantity. But before using it, make sure the units agree.

Unit alignment comes first

A pupil can use the correct formula and still get the wrong answer if distance is in metres while speed is in kilometres per hour, or if time is mixed between minutes and hours.

1 km = 1000 m
1 hour = 60 minutes
30 minutes = 0.5 hour
15 minutes = 0.25 hour

Do the unit conversion before the main calculation unless there is a good reason not to.

Worked example 1: basic speed

Problem: A cyclist travels 18 km in 1.5 hours. What is the average speed?

Speed = Distance ÷ Time = 18 ÷ 1.5 = 12 km/h.

The phrase “average speed” here refers to total distance divided by total time.

Catching-up problems

Catching up happens when two objects move in the same direction and the faster one closes an existing gap.

Relative speed = faster speed − slower speed.

Then: time to catch up = starting gap ÷ relative speed.

Worked example 2: catching up

Problem: Ben leaves at 8.00 am cycling at 12 km/h. Aisha leaves from the same place at 9.00 am cycling along the same route at 18 km/h. When does Aisha catch Ben?

By 9.00 am, Ben has a 12 km head start.

Relative speed = 18 − 12 = 6 km/h.

Catch-up time = 12 ÷ 6 = 2 hours.

Aisha catches Ben at 11.00 am.

Meeting problems

When two travellers move towards each other, the distance between them closes at the sum of their speeds.

Closing speed = speed 1 + speed 2.

Worked example 3: meeting

Problem: Two towns are 210 km apart. Two cars leave at the same time and travel towards each other at 60 km/h and 45 km/h. How long before they meet?

Closing speed = 60 + 45 = 105 km/h.

Time = 210 ÷ 105 = 2 hours.

Same direction versus opposite direction

Same direction: subtract speeds when one is catching the other.
Opposite directions towards each other: add speeds.
Moving apart: add speeds if they start together and separate.
One stationary object: relative speed is simply the moving speed.

The diagram should make the direction obvious before any formula is used.

Average speed: the most common trap

Average speed is total distance ÷ total time. It is not usually the average of two speeds.

Example: A car travels 60 km at 30 km/h and another 60 km at 60 km/h.

Time for first 60 km = 2 h.
Time for second 60 km = 1 h.
Total distance = 120 km.
Total time = 3 h.
Average speed = 120 ÷ 3 = 40 km/h.

The arithmetic mean of 30 and 60 is 45, which is wrong here because the car spends different amounts of time at the two speeds.

Average speed when times are equal

If the traveller spends equal amounts of time at two speeds, the average speed is the arithmetic mean of those speeds.

Example: 1 hour at 30 km/h and 1 hour at 50 km/h gives total distance 80 km over 2 hours, so average speed = 40 km/h.

Journey-table method

For multi-stage trips, use a table with columns:

Stage
Distance
Speed
Time

Fill any known values, calculate missing stage values, then combine total distance and total time only at the end.

Worked example 4: two-stage journey

Problem: A van travels 90 km at 45 km/h, stops for 30 minutes, then travels 120 km at 60 km/h. What is its average speed for the entire trip including the stop?

First travel time = 90 ÷ 45 = 2 h.
Stop = 0.5 h.
Second travel time = 120 ÷ 60 = 2 h.

Total distance = 210 km.
Total time = 4.5 h.
Average speed = 210 ÷ 4.5 = 46⅔ km/h.

If the question excludes stopping time, the denominator changes. Read the scope carefully.

The speed error taxonomy

unit mismatch
wrong direction, so relative speeds are added/subtracted incorrectly
uses average of speeds instead of total distance ÷ total time
forgets a waiting or stopping interval
uses clock time instead of duration
mixes head-start distance with journey distance
solves correctly but answers the wrong time of day

A diagram before calculation

For catching and meeting problems, draw a horizontal route. Mark starting positions, direction arrows, times and the unknown meeting point. For multi-stage journeys, draw separate segments. A ten-second diagram can prevent a five-minute correction.

Transfer practice

Practice 1

Problem structure: A runner travels 10 km in 50 minutes.

Key reasoning: Convert 50 min to 5/6 h; speed = 12 km/h.

Practice 2

Problem structure: Two cyclists 90 km apart ride toward each other at 20 and 25 km/h.

Key reasoning: Closing speed 45; meet in 2 h.

Practice 3

Problem structure: A faster bus at 70 km/h chases a bus at 55 km/h with a 30 km lead.

Key reasoning: Relative speed 15; catch in 2 h.

Practice 4

Problem structure: 40 km at 20 km/h, then 40 km at 40 km/h.

Key reasoning: Total time 2+1=3 h; average speed 80/3 km/h.

Frequently asked questions

When do I add speeds?

When two movers close distance by moving towards each other, or separate in opposite directions.

When do I subtract speeds?

When one mover catches another travelling in the same direction.

How do I calculate average speed?

Total distance divided by total time for the scope named in the question.

Should stops count in average speed?

Only if the question defines the entire elapsed journey that way. Read the wording carefully.

What is the best first step?

Draw the movement and align units.

Where does this sit in Atlas?

This is the canonical Speed owner under PSLE Mathematics Heuristics.

The final Speed rule

Draw the journey before touching the formula. Once direction, distance, time and units are correct, speed problems reduce to a small number of reliable relationships.

Explore the connected learning guides

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Take one question further

The same learning habit can travel across subjects, while each subject keeps its own methods. These routes help you notice a difficulty, understand one part of it, and return to something you can do.

A word is familiar, but using it is difficult.

Move from recognising a word to retrieving it in a new context. Understand vocabulary plateaus.

Try it without the guide: Choose one word you already know. Close the guide and use it in a new sentence. Explain why it fits; try another context tomorrow.

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Make the order of events and the links between sentences clear. Explore composition writing.

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Find the first point where the working stops being reliable. Find Secondary 4 A-Math mark leakage.

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Check the question, source, date and evidence before combining claims. Explore the World Knowledge research library.

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