Speed and Time

Grade 12 Math - Speed and Time

Lesson Objectives

Understand the relationship between speed, distance, and time.
Convert between units of speed and time when necessary.
Solve problems involving average speed and travel time.
Apply the concepts to real-life and exam-based problems.

Lesson Introduction

Speed and time calculations are essential in real-world scenarios like travel planning and logistics. In this lesson, we explore how to compute speed, distance, and time using the basic formula and solve various types of related word problems.

Core Lesson Content

Key Formula

\( \text{Speed} = \frac{\text{Distance}}{\text{Time}} \) \( \text{Distance} = \text{Speed} \times \text{Time} \) \( \text{Time} = \frac{\text{Distance}}{\text{Speed}} \)

Worked Example

Example 1: A car travels 120 km in 3 hours. Find its speed.
\( \text{Speed} = \frac{120}{3} = 40\ \text{km/h} \)

Example 2: How far can a cyclist go in 4 hours at 25 km/h?
\( \text{Distance} = 25 \times 4 = 100\ \text{km} \)

Example 3: A train is moving at 60 km/h. How long will it take to cover 180 km?
\( \text{Time} = \frac{180}{60} = 3\ \text{hours} \)

Example 4: A bus travels 150 km at 50 km/h and then 100 km at 25 km/h. Find the average speed.
Time = \( \frac{150}{50} + \frac{100}{25} = 3 + 4 = 7 \ \text{hours} \)
Total distance = 250 km
Average speed = \( \frac{250}{7} \approx 35.71\ \text{km/h} \)

Example 5: A car moves 90 km in 2 hours and 30 minutes. Find its speed in km/h.
Convert 2 hours 30 minutes to hours: \( 2.5 \ \text{hours} \)
\( \text{Speed} = \frac{90}{2.5} = 36\ \text{km/h} \)

Example 6: [WAEC] A man jogs 8 km every morning in 1 hour 20 minutes. What is his average speed in m/s?
Convert distance to meters: \( 8000 \ \text{m} \), time = \( 1 \times 60 + 20 = 80 \ \text{minutes} = 4800 \ \text{seconds} \)
Speed = \( \frac{8000}{4800} = 1.67 \ \text{m/s} \)

Example 7: A car travels at 72 km/h. Convert this speed to m/s.
\( \text{Speed} = \frac{72 \times 1000}{3600} = 20 \ \text{m/s} \)

Example 8: If a runner maintains a speed of 6 m/s, how far can they run in 15 minutes?
Time = \( 15 \times 60 = 900 \ \text{seconds} \)
Distance = \( 6 \times 900 = 5400 \ \text{meters} = 5.4 \ \text{km} \)

Example 9: A car travels 2.5 km in 3 minutes. Find the speed in km/h.
Time = \( \frac{3}{60} = 0.05 \ \text{h} \)
\( \text{Speed} = \frac{2.5}{0.05} = 50\ \text{km/h} \)

Example 10: A train travels from Lagos to Ibadan, covering 130 km in 2 hours. Find its average speed.
\( \text{Speed} = \frac{130}{2} = 65\ \text{km/h} \)

Exercises

[NECO] A bike covers 75 km in 3 hours. Find the speed. (Past Question)
How long does it take to travel 180 km at a speed of 60 km/h?
A car moves at 90 km/h. How far will it go in 2 hours and 15 minutes?
[WAEC] Convert 54 km/h to m/s. (Past Question)
Calculate the average speed of a journey of 400 km that took 5 hours.
A motorist covered 120 km in 1 hour 30 minutes. What was the speed?
[JAMB] How far can a cyclist go in 40 minutes at 18 km/h? (Past Question)
Find the speed in km/h of a man who jogs 3000 meters in 20 minutes.
[WAEC] A car travels at 33.33 m/s. Convert to km/h. (Past Question)
A train covers 100 km in 1.5 hours. What is its speed?

Conclusion/Recap

Speed, distance, and time are interrelated quantities used in many everyday and technical applications. By mastering the formulas and practicing various problem types, students can confidently solve both theoretical and practical problems involving motion and time.