Solving Problems with the Speed Formula

Lesson 4 of 6: Distance, Time and Speed

In this lesson:

• Derive the formulae for distance and time
• Use the formula triangle to choose the right formula
• Solve problems involving all three quantities

What You Will Learn Today

By the end of this lesson:

1. Derive from the speed formula
2. Derive from the speed formula
3. Apply all three formulae to solve real-life problems
4. Choose the correct formula for each problem
5. Solve problems where any of the three quantities is unknown

Review: A New Type of Problem

From Lesson 3:

Review: A car travels 120 km in 3 hours. Find its speed.

New problem: A matatu goes 50 km/hr for 2 hours. How far?

Can S = D ÷ T find this directly?

Three Things We Might Need to Find

Every distance-speed-time problem gives you two quantities and asks for the third.

Today we derive the two missing formulae.

Deriving Distance = Speed × Time

→ multiply both sides by →

Deriving Time = Distance ÷ Speed

From :

All three formulae from one relationship:

The Formula Triangle: Cover to Find

Draw this triangle and use it for every problem.

Worked Example: Bicycle Travels 15 km/hr

A bicycle travels at 15 km/hr for 3 hours. Find the distance.

Understand: Find distance. S = 15 km/hr, T = 3 hours.

Plan: Use

Work:

Answer: The bicycle travels 45 km.

Worked Example: Bus Journey of 160 km

A bus travels 160 km at 80 km/hr. How long does it take?

Understand: Find time. D = 160 km, S = 80 km/hr.

Plan: Use

Work:

Answer: The journey takes 2 hours.

Quick Check: Use the Triangle

S = 40 km/hr, T = 3 hours. Which formula finds distance? Calculate it.

• Which quantity are you finding?
• Cover it in the triangle — what operation do you see?
• Calculate. Include the unit.

Work it out before advancing.

Quick Check: Distance Formula Answer

Finding D: Cover D in the triangle → see S × T → use

Answer: 120 km

Decision Rule: Choose the Right Formula

Before every problem, ask: What am I finding?

• Finding Speed: use
• Finding Distance: use
• Finding Time: use

Check: Do units match? (km + km/hr → hours; not seconds)

Worked Example: Person Walks 4 km/hr

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:

Work:

Answer: The person walks 12 km.

Worked Example: Car Travels 150 km

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:

Work:

Answer: The journey takes 3 hours.

Worked Example: Boda-Boda Speed Calculation

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

Understand: Find speed. D = 60 km, T = 2 hours.

Plan:

Work:

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

Guided Practice: Find the Distance

A matatu travels at 60 km/hr for 2 hours. Find the distance.

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

Plan: Use

Work:

Answer: The matatu travels ___ km.

Fill in every blank, then advance.

Guided Practice: All Steps Shown

A matatu travels at 60 km/hr for 2 hours.

Understand: Find distance. S = 60 km/hr, T = 2 hours.

Plan:

Work:

Answer: The matatu travels 120 km.

Practice: Solve Four Mixed Problems

Solve using the 4-step method. Show working for each.

1. A car: 80 km/hr for 2 hours. How far?
2. A learner: 8 km at 4 km/hr. How long?
3. A bus: 200 km in 4 hours. What speed?
4. A bicycle: 12 km/hr for 5 hours. Find distance.

Practice: Check Your Working and Answers

Did you identify what to find before calculating?

Quick Check: Bus Journey Time Problem

A bus travels 180 km at 60 km/hr. How long does the journey take?

Show all four steps before advancing.

Quick Check: Journey Time Answer

Understand: Find time. D = 180 km, S = 60 km/hr.

Plan:

Work:

Answer: 3 hours

Key Takeaways from Today's Lesson

✓ One relationship: — all three formulae come from it

✓ Find D: use · Find T: use

✓ Decision rule: read the problem → find the unknown → use the triangle

Always identify what to find before choosing a formula

Units must match: km + km/hr → answer in hours

Always write the unit · Always show all four steps

Next Lesson: Reading Distance-Time Graphs

In Lesson 5, we plot distance against time:

• Straight line → constant speed
• Steeper slope → faster speed

Homework: Copy the formula triangle. Solve 5 problems (a–e) using all four steps.