Page 1 · Introduction
Speed, distance and time
These three quantities are linked by one simple relationship. Once you see how they connect, a whole family of questions opens up — and you'll wonder why they ever looked hard.
- Distance — how far (metres, kilometres).
- Time — how long (seconds, minutes, hours).
- Speed — how fast (km/h, m/s).
The big ideaSpeed = distance ÷ time. Know any two of the three, and you can always find the third.
💡We'll build from easy to challenging, step by step. By the end you'll handle multi-leg journeys and catch-up problems that stump most students.
On the real testWhere this appearsThese problems live in the Mathematical Reasoning section (25% of your mark, computer-based, no calculator from 2025). The mental shortcuts here are exactly what save time on the day.
Page 2 · The theory
The formula triangle
All three formulas come from one triangle. Picture D on top, with S and T underneath:
Speed = Distance ÷ Time
Distance = Speed × Time
Time = Distance ÷ Speed
How to use it
Cover the quantity you want with your finger:
- Cover D → you see S × T → Distance = Speed × Time
- Cover S → you see D over T → Speed = Distance ÷ Time
- Cover T → you see D over S → Time = Distance ÷ Speed
✅Draw the triangle on your scrap paper at the start of the test. It means you never have to remember which formula is which.
Page 3 · The golden rule
Units must match
This is where most marks are lost — and where you can beat other students just by being careful. If speed is in km/h, then time must be in hours, not minutes.
Time conversions to memorise
- 15 minutes = 0.25 hours
- 30 minutes = 0.5 hours
- 45 minutes = 0.75 hours
- 20 minutes = ⅓ hour · 40 minutes = ⅔ hour
Watch this trapA question gives time in minutes but asks for km/h. Convert minutes to hours first, then divide. Forgetting this is the #1 mistake in this topic.
Page 4 · Worked examples
The three jobs, worked through
Every question asks for one of the three. Here's one of each:
Finding SPEED: a car goes 150 km in 2 hours.
Speed = Distance ÷ Time = 150 ÷ 2 = 75.
75 km/h
Finding DISTANCE: a cyclist rides at 20 km/h for 3 hours.
Distance = Speed × Time = 20 × 3 = 60.
60 km
Finding TIME: a train covers 240 km at 80 km/h.
Time = Distance ÷ Speed = 240 ÷ 80 = 3.
3 hours
💡First step on every question: decide which of the three you're looking for. That tells you which formula to use.
Page 5 · A tricky idea
Average speed over a journey
For a trip made of parts, average speed is total distance ÷ total time — NOT the average of the two speeds. This catches almost everyone.
A car drives 60 km in 1 hour, then 60 km in 3 hours. Average speed?
Total distance = 120 km. Total time = 4 hours. 120 ÷ 4 = 30 km/h. (Not the average of 60 and 20!)
30 km/h
RememberNever average the speeds. Always go back to total distance ÷ total time. Write both totals down before you divide.
Page 6 · Finishing cleanly
Turning answers back into minutes
Sometimes your answer comes out as a decimal of an hour, but the question wants minutes. Convert back:
Decimal hours → minutes
- 0.5 hours = 30 minutes
- 0.25 hours = 15 minutes
- 1.5 hours = 1 hour 30 minutes
- ⅓ hour = 20 minutes
A car drives 90 km at 60 km/h. How long, in hours and minutes?
90 ÷ 60 = 1.5 hours = 1 hour 30 minutes.
1 hour 30 minutes
Page 7 · Practice
Level 1 · Easy
Warm up
Straightforward ones to lock in the three formulas. Tap to check.
1. A bus travels 120 km in 3 hours. Average speed?
A 30 km/h
B 360 km/h
C 40 km/h
D 60 km/h
Speed = 120 ÷ 3 = 40 km/h.
2. A plane flies at 500 km/h for 4 hours. How far?
A 125 km
B 2000 km
C 504 km
D 1250 km
Distance = 500 × 4 = 2000 km.
3. A walker covers 12 km at 4 km/h. How long?
Time = 12 ÷ 4 = 3 hours.
🎉Nice — the three formulas are working for you. Now let's add the units twist.
Page 8 · Practice
Level 2 · Medium
Mind the units
Now the times come in minutes. Convert to hours first!
1. A car travels 30 km in 30 minutes. Speed in km/h?
A 60 km/h
B 30 km/h
C 15 km/h
D 900 km/h
30 min = 0.5 h. 30 ÷ 0.5 = 60 km/h. (Trap answer: 30.)
2. A cyclist rides at 15 km/h for 40 minutes. How far?
A 600 km
B 15 km
C 10 km
D 6 km
40 min = ⅔ h. 15 × ⅔ = 10 km.
3. A car drives 90 km at 60 km/h. How long?
90 ÷ 60 = 1.5 hours (1 hour 30 minutes).
💪Units are the difference between right and wrong here. If one caught you, it's a great one to have learned now rather than in the exam.
Page 9 · Practice
Level 3 · Hard
Average speed & scaling
These need the average-speed idea and clever scaling. The trap answers are waiting — avoid them.
1. A car goes 60 km at 60 km/h, then 60 km at 40 km/h. Average speed for the whole trip?
A 50 km/h
B 52 km/h
C 48 km/h
D 45 km/h
Not 50 (that's averaging the speeds). Time = 60/60 + 60/40 = 1 + 1.5 = 2.5 h. 120 ÷ 2.5 = 48 km/h.
2. Priya walks 3 km to school at 6 km/h, then home (3 km) at 4 km/h. Average speed?
A 5 km/h
B 4.8 km/h
C 5.2 km/h
D 4 km/h
Total 6 km. Time = 3/6 + 3/4 = 0.5 + 0.75 = 1.25 h. 6 ÷ 1.25 = 4.8 km/h.
3. A runner does 100 m in 20 seconds. At the same speed, how long for 1 km?
A 200 seconds
B 20 seconds
C 2000 seconds
D 100 seconds
1 km = 1000 m = 10 lots of 100 m. Same speed → 10 × 20 = 200 seconds. Scaling in whole lots beats finding the speed first.
💡These are real exam-level. The average-speed trap fools most students — now it won't fool you.
Page 10 · Challenge
Level 4 · Challenge
Think smart
The toughest tier — these need a real insight. Take your time and don't be put off if they take a few goes.
1. Train A leaves at 60 km/h. One hour later, Train B leaves the same station on the same track at 90 km/h. How long after B departs does it catch A?
A 3 hours
B 2 hours
C 1.5 hours
D 1 hour
In its 1-hour head start, A travels 60 km. B closes the gap at 90 − 60 = 30 km/h. To close 60 km takes 60 ÷ 30 = 2 hours. Thinking in "gap-closing speed" cracks catch-up problems.
2. A car travels 60 km at 30 km/h, then 60 km at 60 km/h. Average speed?
A 40 km/h
B 45 km/h
C 50 km/h
D 30 km/h
Time = 60/30 + 60/60 = 2 + 1 = 3 h. Total 120 km ÷ 3 = 40 km/h. (Averaging the speeds gives 45 — the trap.)
3. A cyclist covers 24 km. If she rode 2 km/h faster, she'd take 1 hour less. Her actual speed leaves her time as 24/speed. If speed = 6, time = 4 h; at 8 km/h, time = 3 h. What is her actual speed?
A 4 km/h
B 8 km/h
C 6 km/h
D 12 km/h
Test the neat pair: at 6 km/h, 24/6 = 4 hours; at 8 km/h (2 faster), 24/8 = 3 hours — exactly 1 hour less. So her actual speed is 6 km/h. Testing sensible whole-number pairs is a smart shortcut when algebra looks scary.
🌟These are beyond most students your age. Every attempt sharpens you — be proud you're tackling them at all.
Complete
Superb work!
You've completed the Speed, Distance & Time module.
From the formula triangle all the way to catch-up problems, you've built a serious toolkit: matching units, average speed, scaling, and gap-closing thinking. Keep practising and these become instinct.