The average speed of a round trip is not the average of the speeds. Let the calculation show it
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Speed, in brief
speed = distance ÷ time (the distance covered per hour, per second). 40 km/h is the speed that covers 40 km in 1 hour.
distance = speed × time time = distance ÷ speed average speed = total distance ÷ total time. It has the same shape as Wednesday's "average = total ÷ count".
1 · Guess, then check
1A driver goes out at 40 km/h and comes back at 60 km/h. What do you think the average speed of the whole round trip is? Write your guess first (it is fine if it is wrong).
The round trip as one strip, each leg as wide as the time it took. Fill in the boxes. The numbers are made up.
2Take each leg as 120 km and check. To fill the boxes in the figure, find:
(1) the time the way out took, in hours;
(2) the time the way back took, in hours.
3How many km is the round trip, and how many hours did it take in all? What is the average speed of the round trip, in km/h?
4Compare your guess in question 1 with the answer to question 3. If they differ, explain in words why, looking at the time spent on the way out and on the way back.
5Now suppose the way out and the way back each took 2 hours, at 40 km/h out and 60 km/h back. What is the average speed of the round trip? What is different from question 3?
2 · In other settings
6On a bicycle, a 4.5 km climb is ridden at 9 km/h and a 4.5 km descent at 18 km/h.
(1) How many hours did the climb and the descent each take?
(2) What is the average speed overall, in km/h?
(3) In a few words, why must you not just do (9 + 18) ÷ 2 = 13.5?
7A 60 m run was split into two halves of 30 m. The first 30 m took 6 seconds and the second 30 m took 4 seconds.
(1) What was the speed in each half, in m/s?
(2) What was the average speed over the whole 60 m, in m/s?
(3) Compare the halfway value of the two speeds in (1), 6.25, with (2), and write what you notice.
3 · Working backwards from the average
8The way out was 90 km at 30 km/h. To make the average speed of the round trip 40 km/h, at what speed must the way back be driven? Draw a diagram and work from the total distance and the total time allowed.
9Corrections 1. From this week's notebook (Tue, Wed, Fri) pick one question you got wrong (or one with no diagram that was not ticked).
(a) which day and number; (b) circle the reason: calculation / diagram / setting up the equation / units / misreading;
(c) redo it with a diagram; (d) a calculation that checks the answer.
5 · One puzzle problem
10[Meeting puzzle for travellers] Two people set off at the same time from P and Q, 2.1 km apart, and walk straight towards each other. The one from P walks 80 m a minute, the one from Q 60 m a minute. Draw a line diagram first, then answer.
(1) How many minutes after setting off do they meet?
(2) How many metres from P do they meet?
How many metres closer do they get in 1 minute? How many metres is 2.1 km?
kids/learn — weekly worksheet. The answers have a page of their own.