Speed and other rates · Grade 8
In Grade 8 you learn: converting units of speed and distance–time graphs.
A rate compares two different quantities, such as kilometres per hour, litres per minute or words per minute. Speed is the most common rate: it links distance, time and how fast something moves.
Key facts
- Speed = distance ÷ time; distance = speed × time; time = distance ÷ speed.
- For km/h, use the time in hours: 15 min = 0.25 h, 20 min = 1/3 h, 45 min = 0.75 h.
- Average speed = total distance ÷ total time — not the average of the speeds.
- km/h → m/s: ÷ 3.6. m/s → km/h: × 3.6.
- On a distance–time graph the gradient is the speed; a flat line means stopped.
- Every rate works the same way: amount = rate × time.
Worked examples
Example 1
A train travels 270 km in 2 hours 15 minutes. What is its average speed?
Answer: 120 km/h
Example 2
Change 72 km/h into m/s.
Answer: 20 m/s