Lesson 15: Average Speed

§Text Passage

1Summary 重點摘要

Average speed = total distance ÷ total time. Don't just average the two speeds! For example, 30 km/h going, 60 km/h returning, average is NOT 45 km/h.

2Vocabulary cards Vocabulary

3Step by step Steps

1. Block 1: Average Speed FormulaThe average speed formula is: average speed = total distance ÷ total time. Remember, it is not the two speeds added and halved! Before calculating, organise the distance and time of every leg, add them all up, and only then divide — the first rule of average speed problems. A small table helps: record each leg's distance and time in separate columns, add everything up, and only then do the final division. Keep the units consistent too: distance in km and time in hours give an average speed in km/h; convert first if the time is given in minutes.
2. Block 2: Basic ExampleExample: a car covers 40 km in 2 hours, then 60 km in 3 hours. Total distance = 40 + 60 = 100 km, total time = 2 + 3 = 5 hours, so average speed = 100 ÷ 5 = 20 km/h. Listing each leg's figures clearly keeps the calculation tidy. Notice that both legs here happen to have the same speed: 40 ÷ 2 = 20 and 60 ÷ 3 = 20, so the average is 20 km/h as well; when the two speeds differ, you must divide total distance by total time instead of averaging the two speeds.
3. Block 3: Going and Returning (Most Common)Going at 30 km/h and returning at 60 km/h — what is the average for the whole trip? Assume the two places are 60 km apart for easy numbers: going time = 60 ÷ 30 = 2 hours, returning time = 60 ÷ 60 = 1 hour. Total distance = 120 km, total time = 3 hours, average = 120 ÷ 3 = 40 km/h. The assumed distance may be any common multiple of 30 and 60, which keeps the numbers easy; whatever you assume, the answer is still 40 km/h.
4. Block 4: Why Not 45?Because the going trip is slow it takes 2 hours, while the fast return takes only 1 hour. The slow leg occupies more time and pulls the average toward itself, so the average speed of 40 km/h sits closer to the slow 30 km/h than to the midpoint 45 km/h. Unequal times mean the average is not in the middle. Only when the two legs take equal time does the average sit exactly halfway between the two speeds; use this feature in a test to check quickly which side your answer should lean towards.
5. Block 5: Known Average, Find DistanceWith average speed and total time known, multiply to find total distance. Example: averaging 50 km/h for 3 hours gives total distance = 50 × 3 = 150 km. This is the average speed formula in reverse: total distance = average speed × total time, just like the speed formula. The units must match one another: with m/min, distances are in m and times in minutes; if the units do not match, convert before calculating, or the result will be completely wrong.
6. Block 6: Known Average, Find TimeWith total distance and average speed known, divide to find total time. Example: for 200 km at an average of 40 km/h, total time = 200 ÷ 40 = 5 hours. The three forms (find the average, the distance, the time) match the speed formula exactly, so one set of skills covers all. Answer in the order of writing the formula, substituting the numbers, then attaching the unit: for example total time = 200 ÷ 40 = 5 hours, and the answer is complete only once the unit 'hours' is written.

4Diagrams Diagrams

5Worked example Example

6Common mistakes Mistakes

7Quick check Quick check

8Recap Recap

• Average speed = total distance ÷ total time
• Don't just average the two speeds
• Slow going, fast returning: average leans to slower
• Assume a distance for easy calculation
• Total distance includes both ways