IGCSE Speed, Distance and Time: Complete Guide for Cambridge IGCSE Mathematics

IGCSE speed, distance and time are fundamental topics in Cambridge IGCSE Mathematics that appear in both Paper 2 and Paper 4. Mastering the speed formula, unit conversions, and average speed calculations is essential for solving real-world problems involving motion and travel.

This comprehensive IGCSE speed, distance and time guide covers everything you need to know, including the relationship between speed, distance and time, unit conversions, average speed over multiple segments, step-by-step worked examples, common exam questions, and expert tips from Tutopiya’s IGCSE maths tutors. We’ll also show you how to avoid the most common mistakes that cost students valuable marks.

🎯 What you’ll learn: By the end of this guide, you’ll know how to calculate speed, distance, and time using the formula triangle, convert between units, find average speed, and apply these skills to solve problems in IGCSE exams.

Already studying with Tutopiya? Practice these skills with our dedicated IGCSE Algebra practice deck featuring exam-style questions and instant feedback.

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Why IGCSE Speed, Distance and Time Matter

IGCSE speed, distance and time are practical topics with real-world applications. Here’s why they’re so important:

• High frequency topic: Speed, distance, and time questions appear regularly in IGCSE maths papers
• Real-world applications: Used in travel planning, physics, and everyday calculations
• Exam weight: Typically worth 4-8 marks per paper
• Foundation for advanced topics: Essential for understanding kinematics and rates of change
• Unit conversion skills: Develops important mathematical reasoning

Key insight from examiners: Students often make errors with unit conversions or forget to use the correct formula. This guide will help you master these systematically.

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The Speed Formula Triangle

The relationship between Speed, Distance, and Time is:

Formula: Speed = Distance ÷ Time

This can be rearranged to find any of the three quantities:

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

The Formula Triangle

     Distance
    ┌─────────┐
    │         │
    │    D    │
    │         │
    ├─────────┤
    │ S   T   │
    └─────────┘

How to use:

• To find Distance: Cover D → D = S × T
• To find Speed: Cover S → S = D ÷ T
• To find Time: Cover T → T = D ÷ S

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Unit Conversions

Time Conversions

• 1 hour = 60 minutes
• 1 minute = 60 seconds
• 1 hour = 3600 seconds

Distance Conversions

• 1 km = 1000 m
• 1 m = 100 cm
• 1 km = 100,000 cm

Speed Units

Common speed units:

• km/h (kilometers per hour)
• m/s (meters per second)
• mph (miles per hour)

Converting Between km/h and m/s

To convert km/h to m/s:

• Divide by 3.6 (or multiply by 1000/3600 = 5/18)

To convert m/s to km/h:

• Multiply by 3.6 (or multiply by 3600/1000 = 18/5)

Why?

• 1 km/h = 1000 m / 3600 s = 5/18 m/s ≈ 0.278 m/s
• 1 m/s = 3600 m / 1000 s = 18/5 km/h = 3.6 km/h

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Calculating Speed

Formula: Speed = Distance ÷ Time

Example 1: A car travels 240 km in 3 hours. Find the average speed.

Solution: Speed = 240 km ÷ 3 hours = 80 km/h

Answer: 80 km/h

Example 2: A runner covers 1500 m in 5 minutes. Find the speed in m/s.

Solution:

1. Convert time: 5 minutes = 5 × 60 = 300 seconds
2. Speed = 1500 m ÷ 300 s = 5 m/s

Answer: 5 m/s

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Calculating Distance

Formula: Distance = Speed × Time

Example 1: A train travels at 90 km/h for 2.5 hours. How far does it travel?

Solution: Distance = 90 km/h × 2.5 hours = 225 km

Answer: 225 km

Example 2: A cyclist rides at 15 m/s for 20 minutes. Find the distance in kilometers.

Solution:

1. Convert time: 20 minutes = 20 × 60 = 1200 seconds
2. Distance: 15 m/s × 1200 s = 18,000 m
3. Convert to km: 18,000 m = 18 km

Answer: 18 km

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Calculating Time

Formula: Time = Distance ÷ Speed

Example 1: How long does it take to travel 300 km at 75 km/h?

Solution: Time = 300 km ÷ 75 km/h = 4 hours

Answer: 4 hours

Example 2: How long does it take to travel 2.4 km at 12 m/s? Give your answer in minutes.

Solution:

1. Convert distance: 2.4 km = 2400 m
2. Time: 2400 m ÷ 12 m/s = 200 seconds
3. Convert to minutes: 200 ÷ 60 = 3.33... minutes = 3 minutes 20 seconds

Answer: 3 minutes 20 seconds or 3 1/3 minutes

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Average Speed

When a journey has multiple segments with different speeds, the average speed is:

Formula: Average Speed = Total Distance ÷ Total Time

Important: Average speed is NOT the average of the individual speeds!

Example: A car travels 60 km at 40 km/h, then 60 km at 60 km/h. Find the average speed.

Solution:

1. Time for first part: 60 km ÷ 40 km/h = 1.5 hours
2. Time for second part: 60 km ÷ 60 km/h = 1 hour
3. Total time: 1.5 + 1 = 2.5 hours
4. Total distance: 60 + 60 = 120 km
5. Average speed: 120 km ÷ 2.5 hours = 48 km/h

Answer: 48 km/h

Note: The average of 40 and 60 is 50, but the actual average speed is 48 km/h because more time was spent at the slower speed.

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Step-by-Step Method for Speed Problems

1. Identify what you need - Speed, distance, or time?
2. Check the units - Convert if necessary
3. Use the correct formula - From the triangle
4. Calculate carefully - Show your working
5. Check your answer - Does it make sense?

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Worked Examples

Example 1: Basic Speed Calculation

A cyclist travels 45 km in 1.5 hours. Find the speed in km/h.

Solution: Speed = 45 km ÷ 1.5 hours = 30 km/h

Answer: 30 km/h

Example 2: Unit Conversion

Convert 72 km/h to m/s.

Solution: 72 km/h = 72 ÷ 3.6 = 20 m/s

Answer: 20 m/s

Example 3: Finding Distance

A plane flies at 800 km/h for 2 hours 15 minutes. How far does it travel?

Solution:

1. Convert time: 2 hours 15 minutes = 2.25 hours
2. Distance: 800 km/h × 2.25 hours = 1800 km

Answer: 1800 km

Example 4: Finding Time

How long does it take to travel 150 km at 60 km/h? Give your answer in hours and minutes.

Solution:

1. Time: 150 km ÷ 60 km/h = 2.5 hours
2. Convert: 2.5 hours = 2 hours 30 minutes

Answer: 2 hours 30 minutes

Example 5: Average Speed

A journey consists of:

• 40 km at 50 km/h
• 60 km at 75 km/h

Find the average speed for the whole journey.

Solution:

1. Time for first part: 40 ÷ 50 = 0.8 hours
2. Time for second part: 60 ÷ 75 = 0.8 hours
3. Total time: 0.8 + 0.8 = 1.6 hours
4. Total distance: 40 + 60 = 100 km
5. Average speed: 100 ÷ 1.6 = 62.5 km/h

Answer: 62.5 km/h

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Common Examiner Traps (and How to Dodge Them)

• Unit conversion errors - Always check units match before calculating
• Time conversion mistakes - Remember: 1 hour = 60 minutes = 3600 seconds
• Average speed confusion - Use total distance ÷ total time, not average of speeds
• Forgetting to convert - Check if answer needs to be in specific units
• Formula errors - Use the triangle to remember which formula to use
• Decimal time - 0.5 hours = 30 minutes, 0.25 hours = 15 minutes

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IGCSE Speed, Distance and Time Practice Questions

Question 1: Basic Calculations

a) Find the speed if distance is 180 km and time is 2.5 hours. b) Find the distance if speed is 65 km/h and time is 3 hours. c) Find the time if distance is 240 km and speed is 80 km/h.

Solution: a) Speed = 180 ÷ 2.5 = 72 km/h b) Distance = 65 × 3 = 195 km c) Time = 240 ÷ 80 = 3 hours

Answers: a) 72 km/h b) 195 km c) 3 hours

Question 2: Unit Conversions

a) Convert 54 km/h to m/s. b) Convert 15 m/s to km/h.

Solution: a) 54 ÷ 3.6 = 15 m/s b) 15 × 3.6 = 54 km/h

Answers: a) 15 m/s b) 54 km/h

Question 3: Average Speed

A car travels 30 km at 40 km/h, then 50 km at 60 km/h. Find the average speed.

Solution:

1. Time 1: 30 ÷ 40 = 0.75 hours
2. Time 2: 50 ÷ 60 = 0.833... hours
3. Total time: 0.75 + 0.833 = 1.583 hours
4. Total distance: 30 + 50 = 80 km
5. Average: 80 ÷ 1.583 = 50.5 km/h (to 1 d.p.)

Answer: 50.5 km/h

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Frequently Asked Questions About IGCSE Speed, Distance and Time

What is the formula for speed?

Speed = Distance ÷ Time. This can be rearranged to find distance (D = S × T) or time (T = D ÷ S).

How do I convert km/h to m/s?

Divide by 3.6. Example: 72 km/h = 72 ÷ 3.6 = 20 m/s.

How do I convert m/s to km/h?

Multiply by 3.6. Example: 15 m/s = 15 × 3.6 = 54 km/h.

How do I find average speed?

Average Speed = Total Distance ÷ Total Time. This is NOT the average of individual speeds!

What if time is given in minutes?

Convert to hours first (divide by 60), or work in minutes and convert distance/speed accordingly.

How do I handle mixed units?

Always convert to the same units before calculating. For example, convert km to m, or hours to seconds.

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Related IGCSE Maths Resources

Strengthen your IGCSE Mathematics preparation with these comprehensive guides:

• IGCSE Rate: Complete Guide - Master rate calculations and comparisons
• IGCSE Ratios and Proportions: Complete Guide - Master ratio simplification and proportion problems
• IGCSE Maths Revision Notes, Syllabus and Preparation Tips - Complete syllabus overview, topic breakdown, and revision strategies
• IGCSE Past Papers Guide - Access free IGCSE past papers and exam resources

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