Distance, Time and Speed: The Formula

Lesson 3 of 6: Distance, Time and Speed

In this lesson:

• Discover why speed = distance ÷ time
• Learn the formula S = D ÷ T
• Use it to calculate speed

What You Will Learn Today

By the end of this lesson:

1. Explain the relationship between distance, time and speed
2. Understand that speed = distance divided by time
3. Derive the formula: Speed = Distance ÷ Time
4. Use the formula to calculate speed
5. Understand: more distance in same time → faster speed

Who Is Faster? John or Mary?

Both walk for exactly 1 hour.

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

Who is faster — and how do you know?

Think before advancing...

John Is Faster — Here Is Why

John covers more distance in the same time.

In 1 hour: John = 6 km, Mary = 4 km → John's speed = 6 km/hr, Mary's = 4 km/hr

Key insight: When time is the same, the larger distance means higher speed.

Discovering the Formula: Step 1

Scenario A: A car travels 60 km in 1 hour. What is its speed?

The car covers 60 km in 1 hour, so its speed is 60 km per hour.

When time = 1 hour, speed equals the distance directly.

Discovering the Formula: Step 2

Scenario B: A car travels 120 km in 2 hours. What is its speed?

In 2 hours it covers 120 km. In 1 hour it covers half that:

Speed = 60 km/hr — same as the Scenario A car!

The Formula: Speed = Distance ÷ Time

We always divide distance by time to find speed:

What S, D, and T Stand For

km + hours → km/hr · m + seconds → m/sec

Quick Check: Use the Formula Now

If two cars both drive for 2 hours, but Car A covers 80 km and Car B covers 100 km:

• Which car is faster?
• Apply the formula to confirm.

Work it out before advancing.

Quick Check: Formula Confirms Car B

Car B is faster — it covers more distance in the same time.

More distance + same time = higher speed. ✓

Worked Example: Bicycle Speed Calculation

A bicycle travels 30 km in 2 hours. Find its speed.

Understand: Find speed. Given D = 30 km, T = 2 hours.

Plan: Use

Work:

Answer: The bicycle's speed is 15 km/hr.

Worked Example: Matatu Speed in Uganda

A matatu travels 80 km in 2 hours. What is its speed?

Understand: Find speed. D = 80 km, T = 2 hours.

Plan:

Work:

Answer: The matatu's speed is 40 km/hr.

Worked Example: A Person's Walking Speed

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

Understand: Find speed. D = 12 km, T = 3 hours.

Plan:

Work:

Answer: The person's speed is 4 km/hr.

Guided Practice: You Try the Four Steps

A car travels 90 km in 3 hours. Find the speed.

Understand: Find ___. D = ___, T = ___.

Plan:

Work:

Answer: The car's speed is ___ km/hr.

Fill in all four steps, then advance.

Guided Practice: All Four Steps Shown

A car travels 90 km in 3 hours.

Understand: Find speed. D = 90 km, T = 3 hours.

Plan:

Work:

Answer: The car's speed is 30 km/hr.

Practice: Calculate Four Different Speeds

Calculate the speed in each case:

1. D = 100 km, T = 2 hours
2. D = 45 km, T = 3 hours
3. D = 200 m, T = 10 seconds
4. A boda-boda travels 60 km in 2 hours.

Show working. Write the unit in every answer.

Practice: Check Your Working and Answers

Problem 3: distance in m, time in sec → speed in m/sec ✓

Quick Check: Final Formula Practice

A car travels 150 km in 3 hours. What is its speed?

Show your working using the four steps.

Solve before advancing.

Quick Check: Speed Formula Answer

Understand: Find speed. D = 150 km, T = 3 hours.

Plan:

Work:

Answer: 50 km/hr

Key Takeaways from Today's Lesson

✓ Speed = Distance ÷ Time

✓ More distance, same time → higher speed

✓ Use 4 steps: Understand → Plan → Work → Answer

Divide distance by time — do NOT add

Match units: km + hours → km/hr · m + sec → m/sec

Always write the unit in your answer

Next Lesson: Rearranging the Formula

In Lesson 4, we rearrange S = D ÷ T to find:

The same triangle — three different arrangements.

Homework: Formula writing, 4 conversions, 2 word problems, and matatu question — in your exercise book.