The Relationship Between Distance, Time and Speed
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P6 Mathematics - Term II

Topic 8: Distance, Time and Speed

Lesson 3: The Relationship Between Distance, Time and Speed

Duration: 45 minutes

Learning Objectives

By the end of this lesson, you will be able to:

  • Explain the relationship between distance, time and speed
  • Understand that speed equals distance divided by time
  • Derive the formula: Speed = Distance ÷ Time
  • Use the formula to calculate speed
  • Recognize that increasing distance increases speed

Quick Review

What we've learned so far:

  • Time units: hours, minutes, seconds
  • Distance units: kilometres, metres
  • Speed units: km/hr, m/sec
  • What does km/hr mean? (kilometres in every hour)

A Speed Question

Two people walk for 1 hour:

  • John walks 6 km in 1 hour
  • Mary walks 4 km in 1 hour

Who is faster?

Answer: Who is Faster?

John is faster!

Why?

  • John covers MORE distance (6 km) in the SAME time (1 hour)
  • His speed: 6 km/hr
  • Mary's speed: 4 km/hr

Key insight: Speed depends on both distance AND time!

The Big Question

How can we find speed?

If we know:

  • Distance traveled
  • Time taken

There must be a way to calculate speed!

Let's discover the formula together.

Exploring the Relationship

Let's look at three scenarios:

Scenario A: Car travels 60 km in 1 hour
Scenario B: Car travels 120 km in 2 hours
Scenario C: Bicycle travels 30 km in 2 hours

How can we find the speed in each case?

Scenario A: Simple Case

Car travels 60 km in 1 hour

  • Distance = 60 km
  • Time = 1 hour
  • Speed = 60 km/hr

That was easy! When time is 1 hour, speed equals the distance.

Scenario B: What If Time is 2 Hours?

Car travels 120 km in 2 hours

Think: In 1 hour, how far does it go?

  • 120 km in 2 hours
  • In 1 hour: 120 ÷ 2 = 60 km
  • Speed = 60 km/hr

We divided distance by time!

Scenario C: Another Example

Bicycle travels 30 km in 2 hours

Calculate:

  • Distance = 30 km
  • Time = 2 hours
  • Speed = 30 ÷ 2 = 15 km/hr

Again, we divided distance by time!

The Formula Revealed!

To find speed, we DIVIDE distance by time

SPEED = DISTANCE ÷ TIME

Using letters:

S = D ÷ T

or

S = D/T

Where: S = Speed, D = Distance, T = Time

Understanding the Formula

S = D ÷ T

What it means:

  • Speed is how much distance you cover per unit of time
  • Dividing distance by time gives us "distance per time"
  • That's exactly what speed is!

The formula makes sense!

Why Division?

Think about it:

  • 60 km in 1 hour = 60 km/hr
  • 60 km in 2 hours = 60 ÷ 2 = 30 km/hr
  • 60 km in 3 hours = 60 ÷ 3 = 20 km/hr

As time increases, speed decreases (if distance stays same)

Using the Formula: Example 1

A matatu travels 80 km in 2 hours. Find its speed.

UNDERSTAND: Find speed; given distance and time
PLAN: Use S = D ÷ T
WORK:

  • S = 80 ÷ 2
  • S = 40 km/hr
    ANSWER: The matatu's speed is 40 km/hr

Using the Formula: Example 2

A person walks 12 km in 3 hours. What is their speed?

UNDERSTAND: Find speed; D = 12 km, T = 3 hours
PLAN: S = D ÷ T
WORK:

  • S = 12 ÷ 3
  • S = 4 km/hr
    ANSWER: The person's walking speed is 4 km/hr

Using the Formula: Example 3

A cyclist covers 200 metres in 10 seconds. Find the speed.

UNDERSTAND: Find speed; D = 200 m, T = 10 sec
PLAN: S = D ÷ T
WORK:

  • S = 200 ÷ 10
  • S = 20 m/sec
    ANSWER: The cyclist's speed is 20 m/sec

Practice Problem 1

Calculate the speed:

Distance = 100 km
Time = 2 hours

Use the formula: S = D ÷ T

Write your answer in your exercise book.

Answer: Practice Problem 1

UNDERSTAND: Find S; D = 100 km, T = 2 hours
PLAN: S = D ÷ T
WORK:

  • S = 100 ÷ 2
  • S = 50
    ANSWER: Speed = 50 km/hr

Did you remember the units?

Practice Problem 2

Calculate the speed:

Distance = 45 km
Time = 3 hours

Show all four steps!

Answer: Practice Problem 2

UNDERSTAND: Find S; D = 45 km, T = 3 hours
PLAN: S = D ÷ T
WORK:

  • S = 45 ÷ 3
  • S = 15
    ANSWER: Speed = 15 km/hr

Understanding the Relationship

Important insights:

  1. If distance increases and time stays same → speed increases
  2. If time increases and distance stays same → speed decreases
  3. Speed connects distance and time mathematically
  4. You need TWO quantities to find the THIRD

The Formula Triangle

A helpful memory tool:

      D
     ___
    |   |
    | S | T
    |___|

To find S: Cover S, you see D ÷ T
We'll learn D and T formulas in the next lesson!

Real-Life Application

Why this formula matters:

  • Calculate how fast vehicles travel
  • Plan journey times
  • Compare different speeds
  • Understand motion in everyday life
  • Foundation for physics and science

Common Mistakes to Avoid

Don't do these:

❌ Forget to divide (just writing the numbers)
❌ Add or multiply instead of divide
❌ Forget the units in your answer
❌ Mix up which is distance and which is time

✅ Always use S = D ÷ T and include units!

Practice Problem 3

A boda-boda travels 60 km in 2 hours. Calculate its speed.

Use the four-step method:

  • UNDERSTAND
  • PLAN
  • WORK
  • ANSWER

Answer: Practice Problem 3

UNDERSTAND: Find speed; D = 60 km, T = 2 hours
PLAN: Use S = D ÷ T
WORK:

  • S = 60 ÷ 2
  • S = 30
    ANSWER: The boda-boda's speed is 30 km/hr

Summary: The Speed Formula

Key points to remember:

  • S = D ÷ T (Speed = Distance ÷ Time)
  • Speed tells us distance per unit of time
  • We DIVIDE distance by time to get speed
  • Always include units in your answer
  • Use the four-step problem-solving method

Why We Derive, Not Just Memorize

NCDC guidance:

"Encourage learners to derive the formula themselves because it will not only stick in their brain, but they will be able to use it appropriately when faced with such problems."

Understanding beats memorization!

Connection to Algebra

This is early algebra!

  • S, D, and T are variables (they can change)
  • We use letters to represent quantities
  • We can rearrange this formula (next lesson!)
  • This prepares you for Topic 12: Algebra in Term III

Homework

Assignment:

  1. Write the speed formula in three ways: in words, using letters, and explain what it means

  2. Calculate speed (show all working):
    a) D = 60 km, T = 2 hours
    b) D = 120 km, T = 4 hours
    c) D = 15 km, T = 3 hours

  3. A bus travels from Kampala to Jinja (80 km) in 2 hours. Calculate its speed.

  4. Two matatus travel for 3 hours. Matatu A covers 120 km, Matatu B covers 90 km. Which is faster? Prove it.

Expected time: 25 minutes

Next Lesson Preview

Tomorrow we will learn:

  • How to rearrange the formula to find Distance
  • How to rearrange the formula to find Time
  • The formula triangle for all three equations
  • Solving problems where you need to find D or T
  • All three formulas: S = D ÷ T, D = S × T, T = D ÷ S

This is exciting!

Credits

Created: January 11, 2026
Based on: NCDC P6 Mathematics Curriculum - Topic 8: Distance, Time and Speed

Source: National Curriculum Development Centre (NCDC), Uganda