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4.3 Using compound measures

4.3 Using compound measures

Compound measures are measures made up of mixed units. For example, ‘kilometres per hour’, ‘miles
per hour’ and ‘metres per second’ are compound measures for speed.

You can use compound measures to make comparisons in real life. For example, you can compare
speeds of cars to see which car can travel fastest.
You can also use compound measures, such as ‘cents per gram’ or ‘cents per litre’, to compare prices of

products. !is means you can work out which items are best value for money.

Worked example 4.3
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1
a A train travels 185 km in 1 hours. A different train travels 500 km in 3 hours.
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2
Which train travels faster?
b A 250 g jar of coffee costs $6.75. A 100 g jar of the same coffee costs $2.68.
Which jar of coffee is better value for money?
185 distance
a Speed of 1st train = Use the formula speed = to work out the speed
125 time
.
1
= 148 km/h of the fi rst train. 1 hours = 1.25 hours.
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500
Speed of 2nd train = 35 Work out the speed of the second train.
.
= 142.9 km/h Round the answer to a suitable degree of accuracy
e.g. one decimal place.
The 1st train is faster. Compare the speeds and write down which is faster.
b $6.75 ÷ 2.5 = $2.70 Divide $6.75 by 2.5 to work out the cost per 100 g of coffee.
1st jar costs $2.70 per 100 g. You could compare the costs per gram, per 50 g, per 500 g, etc.
2nd jar costs $2.68 per 100 g. It doesn’t matter which measure you choose to compare as long as
2nd jar is better value for money. it is the same for both items.

) Exercise 4.3 For each question in this exercise show all your working and check your answers.

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1
1 A train travels 420 km in 2 hours. Another train travels 530 km in 3 hours.
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2
Which train travels faster?
2 Pierre drove from Paris to Bordeaux. The total distance was 584 km.
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3
He drove the first 242 km in 2 hours. He drove the rest of the way in 3 hours.

4 4

Was he travelling faster during the first part of the journey or the second?
3 Sally is training for a marathon. She goes for a run every Tuesday and Friday evening.
Last week, on Tuesday she ran 2.4 km in 18 minutes. On Friday she ran 1.8 km in 12 minutes.
a Work out the speed Sally ran each evening, in kilometres per minute.
b On which evening did Sally run faster?

4 A pack of four toilet rolls costs $2.28. A pack of nine of the same toilet rolls costs $4.95.
a Work out the cost per roll for each pack.
b Which pack is the better value for money?
5 A 750 ml bottle of FabCo costs $1.80. A 1.4 litre bottle of FabCo costs $3.50.
a Work out the cost for each bottle, in cents per millilitre.
b Which bottle is better value for money?

38 4 Length, mass, capacity and time