Speed and other rates · Grade 8

In Grade 8 you learn: converting units of speed.

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.
  • 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

How long does it take to cycle 18 km at 12 km/h? Give your answer in hours and minutes.

Answer: 1 hour 30 minutes

Example 3

Change 72 km/h into m/s.

Answer: 20 m/s

Example 4

A coach drives for 2 hours at 60 km/h, then 1.5 hours at 100 km/h. Find the average speed for the whole journey, to 1 decimal place.

Answer: 77.1 km/h

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