P6 Mathematics - Term II

Topic 8: Distance, Time and Speed

Lesson 4: Solving Problems Using the Speed Formula

Duration: 45 minutes

Learning Objectives

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

• Rearrange the speed formula to find distance
• Rearrange the speed formula to find time
• Use all three formulae to solve problems
• Choose the correct formula based on what you need to find
• Solve multi-step problems involving distance, time and speed

Review: The Speed Formula

What we learned yesterday:

S = D ÷ T

Speed = Distance ÷ Time

Example: A car travels 120 km in 3 hours

• S = 120 ÷ 3 = 40 km/hr

A New Type of Problem

What if we know speed and time, but need to find distance?

Example: A matatu travels at 50 km/hr for 2 hours. How far does it go?

Given: Speed = 50 km/hr, Time = 2 hours
Find: Distance = ?

Can we use S = D ÷ T? Not directly!

Thinking Through the Matatu Problem

What we know:

• Speed = 50 km/hr means 50 km in every hour
• Time = 2 hours

Logical thinking:

• In 1 hour: 50 km
• In 2 hours: 50 km + 50 km = 100 km
• Or: 50 × 2 = 100 km

The matatu travels 100 km

Discovering the Distance Formula

From the matatu problem, we saw:

• Distance = 50 × 2
• Distance = Speed × Time

The formula for distance is:

D = S × T

Distance = Speed × Time

We multiply!

Why Does D = S × T Make Sense?

Think about it:

If you travel at 40 km/hr:

• For 1 hour: D = 40 × 1 = 40 km
• For 2 hours: D = 40 × 2 = 80 km
• For 3 hours: D = 40 × 3 = 120 km

More time = more distance (at same speed)

Using the Distance Formula

Example: A person walks at 4 km/hr for 3 hours. How far do they walk?

UNDERSTAND: Find distance; S = 4 km/hr, T = 3 hours
PLAN: Use D = S × T
WORK:

• D = 4 × 3
• D = 12 km
  ANSWER: The person walks 12 km

Another Distance Example

Example: A bicycle travels at 12 km/hr for 5 hours. Find the distance.

UNDERSTAND: Find D; S = 12 km/hr, T = 5 hours
PLAN: D = S × T
WORK:

• D = 12 × 5
• D = 60 km
  ANSWER: The bicycle travels 60 km

Now Another Challenge!

What if we know distance and speed, but need to find time?

Example: A bus travels 160 km at a speed of 80 km/hr. How long does it take?

Given: Distance = 160 km, Speed = 80 km/hr
Find: Time = ?

Let's think through this...

Thinking Through the Bus Problem

What we know:

• Speed = 80 km/hr means 80 km in every hour
• Distance = 160 km

Logical thinking:

• If 80 km takes 1 hour
• Then 160 km takes 160 ÷ 80 = 2 hours

The journey takes 2 hours

Discovering the Time Formula

From the bus problem, we saw:

• Time = 160 ÷ 80
• Time = Distance ÷ Speed

The formula for time is:

T = D ÷ S

Time = Distance ÷ Speed

We divide distance by speed!

Why Does T = D ÷ S Make Sense?

Think about it:

To travel 120 km:

• At 60 km/hr: T = 120 ÷ 60 = 2 hours
• At 40 km/hr: T = 120 ÷ 40 = 3 hours
• At 30 km/hr: T = 120 ÷ 30 = 4 hours

Faster speed = less time (for same distance)

Using the Time Formula

Example: A car travels 150 km at 50 km/hr. How long does it take?

UNDERSTAND: Find time; D = 150 km, S = 50 km/hr
PLAN: Use T = D ÷ S
WORK:

• T = 150 ÷ 50
• T = 3 hours
  ANSWER: The journey takes 3 hours

The Three Formulae Together

Now we have all three!

S = D ÷ T  (Speed = Distance ÷ Time)
D = S × T  (Distance = Speed × Time)
T = D ÷ S  (Time = Distance ÷ Speed)

Choose the formula based on what you need to find!

The Formula Triangle

A helpful memory tool:

      D
     ___
    |   |
    | S | T
    |___|

• Cover D: See S × T → D = S × T
• Cover S: See D ÷ T → S = D ÷ T
• Cover T: See D ÷ S → T = D ÷ S

How to Use the Triangle

Step 1: Identify what you need to find (D, S, or T)
Step 2: Cover that letter in the triangle
Step 3: Use what you see as your formula
Step 4: Solve using the four-step method

Practice using the triangle!

Mixed Practice Problem 1

A matatu travels at 60 km/hr for 2 hours. How far does it go?

What do we need to find? Distance
What's the formula? D = S × T

Solve it in your exercise book!

Answer: Practice Problem 1

UNDERSTAND: Find D; S = 60 km/hr, T = 2 hours
PLAN: D = S × T
WORK:

• D = 60 × 2
• D = 120 km
  ANSWER: The matatu travels 120 km

Did you use the triangle?

Mixed Practice Problem 2

A learner walks 8 km at 4 km/hr. How long does it take?

What do we need to find? Time
What's the formula? T = D ÷ S

Your turn to solve!

Answer: Practice Problem 2

UNDERSTAND: Find T; D = 8 km, S = 4 km/hr
PLAN: T = D ÷ S
WORK:

• T = 8 ÷ 4
• T = 2 hours
  ANSWER: The walk takes 2 hours

Well done if you got this correct!

Mixed Practice Problem 3

A bus travels 200 km in 4 hours. What is its speed?

What do we need to find? Speed
What's the formula? S = D ÷ T

Go ahead and solve!

Answer: Practice Problem 3

UNDERSTAND: Find S; D = 200 km, T = 4 hours
PLAN: S = D ÷ T
WORK:

• S = 200 ÷ 4
• S = 50 km/hr
  ANSWER: The bus's speed is 50 km/hr

You're becoming an expert!

Choosing the Right Formula

The secret: Look at what you're given and what you need

Given D and T, Find S → S = D ÷ T
Given S and T, Find D → D = S × T
Given D and S, Find T → T = D ÷ S

Read the problem carefully!

A Real-Life Problem

A bus leaves Kampala for Mbarara (240 km) traveling at 60 km/hr.

Question 1: How long will the journey take?
Question 2: If it leaves at 8:00 a.m., what time will it arrive?

Think about both questions!

Solution: Real-Life Problem

Part 1: Find time

• T = D ÷ S = 240 ÷ 60 = 4 hours

Part 2: Find arrival time

• Departure: 8:00 a.m.
• Journey time: 4 hours
• Arrival: 8:00 + 4:00 = 12:00 noon

The bus arrives at noon!

Summary: Three Powerful Formulae

Remember these:

S = D ÷ T  (to find Speed)
D = S × T  (to find Distance)
T = D ÷ S  (to find Time)

Use the triangle to remember!
Always show your four-step working!

Why These Formulae Matter

These formulae help us:

• Plan journeys and estimate arrival times
• Compare different speeds and distances
• Make decisions about transportation
• Understand motion in the world around us
• Build foundation for physics in secondary school

Common Mistakes to Avoid

Don't do these:

Use the wrong formula (check what you're finding!)
Multiply when you should divide
Forget units in your answer
Skip the four-step method

Use the triangle, choose correctly, show all working!

Homework

Assignment:

1. Copy the formula triangle and all three formulae

2. Solve these (show all working):
   a) Matatu: 50 km/hr for 3 hours → Find distance
   b) Learner: walks 10 km at 5 km/hr → Find time
   c) Bus: 240 km in 4 hours → Find speed

3. A bus leaves Kampala at 8:00 a.m. traveling to Mbarara (240 km) at 60 km/hr. Find the time taken and arrival time.

4. Two cars travel 80 km. Car A takes 2 hours, Car B takes 4 hours. Calculate each speed. Which is faster?

Expected time: 30 minutes

Next Lesson Preview

Tomorrow we will learn about:

• Distance-time graphs
• How to read information from graphs
• What different graph shapes mean
• Understanding constant speed and rest on graphs
• Visual representation of journeys

Bring your ruler and exercise book!

Credits

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

Source: National Curriculum Development Centre (NCDC), Uganda