Average speed

1Summary 重點摘要

Average speed = total distance ÷ total time.

2Vocabulary cards Vocabulary

3Step by step Steps

1. Step 1: The formulaAverage speed = total distance ÷ total time. For 100 km covered in 2 hours the average speed is 100 ÷ 2 = 50 km/h. The key word is total: all the distances add up, and so do all the times; both totals are used. Why stress the total? Because average speed describes the whole journey, spreading the entire distance across the entire time, not the rate of any single leg. A common error is leaving out one leg of the distance or the time and dividing with a partial amount; before writing the working, list every leg's distance and time and confirm nothing is missing.
2. Step 2: A single-leg caseWith one leg only, the formula is at its simplest: 100 km divided by 2 hours gives 50 km/h. A single leg's average speed is just its speed, found by one division. This is the basic case, and the multi-leg cases later all grow out of it; master the single leg first and the rest follows. Why is a single leg especially simple? Because the total distance and the total time are exactly this leg's own figures, and nothing needs merging. A common mistake is misreading the unit: km/h means kilometres travelled per hour; always write the full unit in the answer, since a bare number loses marks.
3. Step 3: Add the distancesThe total distance is the sum of every leg: going 60 km in 2 hours and returning 40 km in 1 hour gives total distance = 60 + 40 = 100 km. Outbound or homebound, every kilometre travelled belongs to the total, and no leg may be left out. Why include everything? Because average speed describes the whole trip, and every kilometre driven spent time, so distances and times must come as a complete pair. A common error is counting only the outward or only the return leg, such as taking 60 km as the total, which inflates the speed found later; ask first how many legs there are, list them, then add.
4. Step 4: Add the timesThe total time adds up in the same way: total time = 2 + 1 = 3 hours. The time going and the time returning are both spent on the trip and must merge. Why can no part be dropped? Because losing any stretch of time shrinks the divisor and inflates the average speed; missing the return's 1 hour gives 100 ÷ 2 = 50 km/h, far above the correct 33.3 km/h. The typical mistake is exactly this omission, and time spent stopping or resting counts too; think how long the trip took from departure to arrival, and nothing will be left out.
5. Step 5: DivideDivide the two totals: total distance 100 ÷ total time 3 ≈ 33.3 km/h. When the division does not end, keep one decimal place and write the approximation sign for an approximate value. This number tells how far the whole trip goes per hour on average, the representative rate of the entire journey. Why the approximation sign? Because 100 ÷ 3 is a recurring decimal and 33.3 is only an approximation; an equals sign would mislead the reader into thinking it is exact. A common error is keeping an approximate value but writing =, or using different numbers of decimal places; follow the required precision and remember both the sign and the unit.
6. Step 6: Know the trapRecognise the classic trap: leg speeds 60 out and 40 back must not be averaged as (60 + 40) ÷ 2 = 50, because the two legs take different times — the outward 60 km took 2 hours while the return 40 km took only 1 hour, so the longer leg weighs more in the average. Direct averaging is allowed only when the two times are equal: 40 km in the first hour and 60 km in the second genuinely give (40 + 60) ÷ 2 = 50. The common error is averaging the speeds straight away; remember that average speed must always come from the total distance divided by the total time.

4Diagrams Diagrams

5Worked example Example

6Common mistakes Mistakes

7Quick check Quick check

8Recap Recap

• Average speed = total distance ÷ total time
• Never average two leg speeds directly (times differ)
• Direct averaging works only for equal times
• Unify time units first (minutes → hours)
• Check: average speed × total time = total distance