How do you calculate speed using distance and time in Cambridge IGCSE Mathematics?

In Cambridge IGCSE Mathematics, speed is calculated using the formula: Speed = Distance ÷ Time. This formula helps determine how fast an object is moving by dividing the distance traveled by the time taken to travel that distance.

What is the relationship between speed, distance, and time?

The relationship between speed, distance, and time is expressed through the formula: Distance = Speed × Time. This formula indicates that distance is the product of speed and time, showing how far an object travels at a certain speed over a given period.

How can I solve problems involving average speed in the IGCSE curriculum?

To solve problems involving average speed in the IGCSE curriculum, use the formula: Average Speed = Total Distance ÷ Total Time. This involves calculating the total distance traveled and dividing it by the total time taken, which gives the average speed over the entire journey.

What units are commonly used for speed, distance, and time in IGCSE Mathematics?

In IGCSE Mathematics, speed is typically measured in meters per second (m/s) or kilometers per hour (km/h), distance in meters (m) or kilometers (km), and time in seconds (s) or hours (h). It's important to ensure consistency in units when solving problems.

How do you convert between different units of speed, such as from m/s to km/h?

To convert speed from meters per second (m/s) to kilometers per hour (km/h), multiply the speed by 3.6. Conversely, to convert from km/h to m/s, divide the speed by 3.6. This conversion is essential for solving problems where different units are used.

Why is "Using mixed units in $d = s \times t$ without converting" a common mistake in Speed, Distance and Time?

Why it happens: Students plug in km/h and minutes together. How to avoid it: Convert the time to the same unit base as the speed (e.g. hours for km/h). Source: 0580 examiner reports — recurring

Why is "Averaging two speeds to get average speed" a common mistake in Speed, Distance and Time?

Why it happens: It feels intuitive: 60 + 90/2 = 75. How to avoid it: Always use total distance ÷ total time. The average happened to equal 75 in our example by coincidence — don't rely on it. Source: 0580/42 May/Jun 2023 — examiner report Q5

Why is "Misconverting decimal hours to minutes" a common mistake in Speed, Distance and Time?

Why it happens: 0.3 h is read as 30 min instead of 18 min. How to avoid it: Multiply the decimal part by 60 to convert to minutes.

Why is "Rearranging the speed–distance–time triangle incorrectly" a common mistake in Speed, Distance and Time?

Why it happens: Students don't memorise the triangle and try to reverse-engineer. How to avoid it: Memorise: D on top, S and T underneath. Cover the unknown to read off the formula.

NumberCambridge IGCSE Mathematics (0580)

Speed, Distance and Time

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Speed, Distance and Time — Cambridge IGCSE 0580 Maths Extended (2026)

One formula triangle, three rearrangements, and constant unit conversions — that's the whole topic. Where students lose marks: km/h vs m/s, and using individual-leg speeds in 'average speed' questions.

At a glance

$\text{speed} = \dfrac{\text{distance}}{\text{time}}$ , $\text{distance} = \text{speed} \times \text{time}$ , $\text{time} = \dfrac{\text{distance}}{\text{speed}}$ .
Use a triangle: $D$ on top, $S$ and $T$ at the bottom — cover what you want.
Convert units BEFORE substituting: km/h vs m/s, hours vs minutes.
$1 \text{ km/h} = \dfrac{1000}{3600} \text{ m/s} = \dfrac{1}{3.6} \text{ m/s}$ .
Average speed for a journey is TOTAL distance $\div$ TOTAL time. NEVER the average of the segment speeds.
Convert minutes to hours by dividing by $60$ . Convert hours to seconds by $\times 3600$ .
Read distance-time graphs: gradient = speed; horizontal segment = stationary.

What you’ll learn

Mapped to the Cambridge IGCSE 0580 syllabus (2025-2027).

E1.16 — Use given data to solve problems on personal and household finance, including earnings, simple interest and compound interest, and motion at constant speed.
Calculate average speed for a journey and convert between km/h and m/s.
Read and interpret distance-time and speed-time graphs.

The formula triangle

One picture handles all three rearrangements. Cover the unknown to read off the formula.

The relationship $D = S \times T$ (distance = speed × time) gives three formulas:

$S = \dfrac{D}{T}, \quad D = S \times T, \quad T = \dfrac{D}{S}.$

Picture them as a triangle with $D$ on top and $S, T$ side-by-side underneath:

    D
  -----
  S | T

Cover whichever you want; the rest is what you do with the others.

Cover $D$ → $D = S \times T$ .
Cover $S$ → $S = D / T$ .
Cover $T$ → $T = D / S$ .

Always check the units match BEFORE substituting.

$D = S \times T$ .
$S = D \div T$ .
$T = D \div S$ .
Cover the unknown — the rest is the formula.

Unit conversions — km/h ↔ m/s, mins ↔ h

More marks are lost on units in this topic than on the formula itself.

Distance and speed must use the SAME unit before substitution.

Time conversions.

$1\,\text{h} = 60\,\text{min} = 3600\,\text{s}$ .
Convert minutes to hours: divide by $60$ . So $45\,\text{min} = 0.75\,\text{h}$ .
Convert seconds to hours: divide by $3600$ .

Speed conversions. $1\,\text{km/h} = \dfrac{1000\,\text{m}}{3600\,\text{s}} = \dfrac{1}{3.6}\,\text{m/s} \approx 0.278\,\text{m/s}.$

In practice:

km/h to m/s: divide by $3.6$ .
m/s to km/h: multiply by $3.6$ .

Worked. A car travels $90\,\text{km/h}$ . Express in m/s.

$90 \div 3.6 = 25\,\text{m/s}$ .

Worked. A runner's speed is $8\,\text{m/s}$ . Express in km/h.

$8 \times 3.6 = 28.8\,\text{km/h}$ .

Mixed-unit traps. "A train travels $48\,\text{km}$ in $40\,\text{minutes}$ . Find its speed in km/h."

$40\,\text{min} = \dfrac{40}{60}\,\text{h} = \dfrac{2}{3}\,\text{h}$ .
$S = 48 \div \dfrac{2}{3} = 48 \times \dfrac{3}{2} = 72\,\text{km/h}$ .

$60\,\text{min} = 1\,\text{h}$ . $3600\,\text{s} = 1\,\text{h}$ .
km/h to m/s: $\div 3.6$ .
m/s to km/h: $\times 3.6$ .
Convert FIRST, substitute SECOND.

Average speed — the trap

Average speed for a journey is total distance over total time. Don't average the segment speeds.

Average speed for a complete journey is $\bar{S} = \dfrac{\text{total distance}}{\text{total time}}.$

This is a TIME-WEIGHTED average. It is NOT the simple mean of the segment speeds.

Worked example (the trap). A driver travels $60\,\text{km}$ at $60\,\text{km/h}$ then $60\,\text{km}$ at $30\,\text{km/h}$ . Find the average speed.

Wrong (simple average): $\dfrac{60 + 30}{2} = 45\,\text{km/h}$ . Wrong by 5 km/h.

Right (total distance / total time):

Time for leg 1: $60 / 60 = 1\,\text{h}$ .
Time for leg 2: $60 / 30 = 2\,\text{h}$ .
Total distance: $120\,\text{km}$ .
Total time: $3\,\text{h}$ .
Average speed: $120 / 3 = 40\,\text{km/h}$ .

The slower leg counts MORE because more time was spent on it.

A quick sanity check. Average speed across a journey is always between the minimum and maximum segment speeds. If your answer is outside that range, recheck.

Average speed = TOTAL distance / TOTAL time.
NEVER average the segment speeds directly.
Compute time for each leg first, sum, then divide total distance.
Average speed is between the min and max of segment speeds.

Distance-time and speed-time graphs

Graphs translate motion into picture form. Read the gradients and areas to recover speed and distance.

Distance-time graphs. Time on the $x$ -axis, distance on the $y$ -axis.

A straight line = constant speed.
A horizontal line = stationary (no distance change).
The gradient equals the speed: $\dfrac{\Delta d}{\Delta t}$ .
A steeper line = faster.
A line returning toward the $x$ -axis = moving back toward the start.

Worked. "On a $d$ - $t$ graph, a runner covers $400\,\text{m}$ in $80\,\text{s}$ as a straight line. Find the speed."

Gradient: $400 / 80 = 5\,\text{m/s}$ .

Speed-time graphs. Time on the $x$ -axis, speed on the $y$ -axis.

A straight horizontal line = constant speed.
A horizontal line at speed $0$ = stationary.
The gradient equals acceleration.
The area UNDER the line equals the distance travelled.

Worked. A vehicle runs at $20\,\text{m/s}$ for $5\,\text{s}$ , then decelerates uniformly to rest in $4\,\text{s}$ . Find the total distance.

Constant section is a rectangle: $20 \times 5 = 100\,\text{m}$ .
Deceleration is a triangle: $\dfrac{1}{2} \times 4 \times 20 = 40\,\text{m}$ .
Total: $140\,\text{m}$ .

$d$ - $t$ graph gradient = speed.
$s$ - $t$ graph gradient = acceleration; area under = distance.
Horizontal $d$ - $t$ = stationary.
Steeper line = faster motion.

How it’s examined

Speed-distance-time questions appear on every paper. Paper 2 typically has a one-step calculation (1-2 marks), often with a unit-conversion sting. Paper 4 escalates to a multi-leg journey or a graph interpretation (3-4 marks). Examiner reports flag two recurring slips: forgetting to convert minutes to hours before dividing, and computing average speed as the arithmetic mean of segment speeds.

Sources: Cambridge IGCSE Mathematics 0580 syllabus 2025-2027 (E1.16); 0580/22 May/Jun 2024 — Q7 (km/h to m/s); 0580/42 Oct/Nov 2024 — Q6 (average speed multi-leg); 0580 Examiner Reports 2022-2024. Last reviewed 2026-05-05.

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Step-by-step worked examples — Speed, Distance and Time

Step-by-step solutions to past-paper-style questions on speed, distance and time, written exactly the way a tutor would explain them at the board.

1Find distance from speed and time
Core• distance
Question
A car travels at $72\,\text{km/h}$ for $2\,\text{h}\ 15\,\text{min}$ . How far does it travel?
Step-by-step solution
1. Step 1
  Convert time to hours: $2\,\text{h}\ 15\,\text{min} = 2.25\,\text{h}$ .
2. Step 2
  Use $d = s \times t$ .
  $d = 72 \times 2.25 = 162\,\text{km}$
Answer
$162\,\text{km}$
2Convert speed between m/s and km/h
Extended• Adapted from 0580/22 Oct/Nov 2023 Q12• unit conversion
Question
Convert $25\,\text{m/s}$ to km/h.
Step-by-step solution
1. Step 1
  $1\,\text{m/s} = 3.6\,\text{km/h}$ (multiply by $3.6$ ).
2. Step 2
  $25 \times 3.6 = 90\,\text{km/h}$ .
Answer
$90\,\text{km/h}$
Examiner tip
Memorise the multipliers: m/s → km/h multiply by $3.6$ ; km/h → m/s divide by $3.6$ .
3Find average speed for a multi-leg journey
Extended• Adapted from 0580/42 May/Jun 2023 Q5• average speed
Question
A train travels $120\,\text{km}$ at $60\,\text{km/h}$ then $180\,\text{km}$ at $90\,\text{km/h}$ . Find the average speed for the whole journey.
Step-by-step solution
1. Step 1
  Time leg 1: $\dfrac{120}{60} = 2\,\text{h}$ .
2. Step 2
  Time leg 2: $\dfrac{180}{90} = 2\,\text{h}$ .
3. Step 3
  Total distance: $300\,\text{km}$ . Total time: $4\,\text{h}$ .
4. Step 4
  Average speed.
  $\dfrac{300}{4} = 75\,\text{km/h}$
Answer
$75\,\text{km/h}$
Examiner tip
Average speed is never the average of the two speeds — always total distance over total time.
4Find time given distance and speed (mixed units)
Core• time, unit conversion
Question
A cyclist covers $7.5\,\text{km}$ at an average speed of $25\,\text{km/h}$ . How long does the journey take, in minutes?
Step-by-step solution
1. Step 1
  Time in hours: $\dfrac{7.5}{25} = 0.3\,\text{h}$ .
2. Step 2
  Convert to minutes: $0.3 \times 60 = 18$ .
Answer
$18$ minutes

Key Formulae — Speed, Distance and Time

The formulae you need to memorise for speed, distance and time on the Cambridge IGCSE 0580 paper, with every variable defined in plain English and a note on when to use it.

Speed–distance–time triangle
$s = \dfrac{d}{t},\quad d = s \times t,\quad t = \dfrac{d}{s}$
$s$
speed
$d$
distance
$t$
time
When to use
Any speed/distance/time question — pick the rearrangement that matches what's asked.
Average speed
$\text{average speed} = \dfrac{\text{total distance}}{\text{total time}}$
When to use
Multi-leg journeys; never average the speeds directly.
m/s ↔ km/h conversion
$v\,\text{m/s} \times 3.6 = v\,\text{km/h}$
$v$
speed value
When to use
Whenever you must compare speeds across different units.

Key Definitions and Keywords — Speed, Distance and Time

Definitions to memorise and the exact keywords mark schemes credit for speed, distance and time answers — sharpened from recent examiner reports for the 2026 0580 sitting.

Speed
Examiner keyword
Distance travelled per unit time (e.g. km/h, m/s).
Average speed
Examiner keyword
Total distance divided by total time for the whole journey.
Velocity
Speed in a specific direction; appears in motion graph problems.
Distance
The length travelled along the path.
Displacement
Straight-line distance from start to end (with direction).

Common Mistakes and Misconceptions — Speed, Distance and Time

The traps other students keep falling into on speed, distance and time questions — taken from recent Cambridge IGCSE 0580 examiner reports and mark schemes — and how to avoid them.

✕Using mixed units in $d = s \times t$ without converting
0580 examiner reports — recurring
Why it happens
Students plug in km/h and minutes together.
How to avoid it
Convert the time to the same unit base as the speed (e.g. hours for km/h).
✕Averaging two speeds to get average speed
0580/42 May/Jun 2023 — examiner report Q5
Why it happens
It feels intuitive: $\dfrac{60 + 90}{2} = 75$ .
How to avoid it
Always use total distance ÷ total time. The average happened to equal $75$ in our example by coincidence — don't rely on it.
✕Misconverting decimal hours to minutes
Why it happens
$0.3$ h is read as $30$ min instead of $18$ min.
How to avoid it
Multiply the decimal part by $60$ to convert to minutes.
✕Rearranging the speed–distance–time triangle incorrectly
Why it happens
Students don't memorise the triangle and try to reverse-engineer.
How to avoid it
Memorise: $D$ on top, $S$ and $T$ underneath. Cover the unknown to read off the formula.

Practice questions

Exam-style questions with step-by-step worked solutions. Try one before checking the method.

Past paper style quiz

Get a report showing which sub-topics you've nailed and which ones still need work.

Video lesson

Short walkthrough of the concepts students most often get stuck on.

Speed, Distance and Time — frequently asked questions

The things students keep getting wrong in this sub-topic, answered.

Speed, Distance and Time

Short Study Notes in the form of Slides

Detailed Study Notes

What you’ll learn

How it’s examined

1Find distance from speed and time

2Convert speed between m/s and km/h

3Find average speed for a multi-leg journey

4Find time given distance and speed (mixed units)

Speed–distance–time triangle

Average speed

m/s ↔ km/h conversion

Speed

Average speed

Velocity

Distance

Displacement

✕Using mixed units in d=s×td = s \times td=s×t without converting

✕Averaging two speeds to get average speed

✕Misconverting decimal hours to minutes

✕Rearranging the speed–distance–time triangle incorrectly

Practice questions

Past paper style quiz

Assess your understanding

Video lesson

Speed, Distance and Time — frequently asked questions

✕Using mixed units in $d = s \times t$ without converting