A rate is a ratio between two measurements with different units. A common example of a rate is speed (which is written in kilometres per hour or km/h). You can see that this describes a relationship between two measurements - kilometres and hours.

We've started to look at how to simplify rates, and now we are going simplify and compare different rates. This is really helpful in everyday life because we can determine things like which car is faster, which shop is offering a better deal and even which job pays more!

Remember!

We need a common point of comparison between two rates to compare them. This is usually done by making the second quantity in the rates equal.

For example, if Steve earns $\$157.05$$157.05 for working $9$9 hours over the weekend and Tina earns $\$144.40$$144.40 for working $8$8 hours, who has the better rate of pay?

To work this out, we need a common point of comparison; we need to work out how much each person earns per hour.

Steve:	$\$157.05$$157.05/$9$9 hrs	$=$=	$\$17.45$$17.45/hr

Tina:	$\$144.40$$144.40/$8$8 hrs	$=$=	$\$18.05$$18.05/hr

So, now we can say with certainty that Tina's rate of pay is higher than Steve's.

Practice questions

Question 1

$Peter$ runs daily and usually covers his $19$19 km in $75$75 minutes.

He also enters half marathon and full marathon events. The last time he ran the $Sydney$ $half marathon$ , an event $21$21 km in length, it took him $126$126 minutes.

What is his running rate during his daily run?
What was his running rate during the $half marathon$ ?
In which event was he running faster on average?
On his daily run.
A
In the $half marathon$ .
B

Question 2

$Neville$ is deciding between four cars to buy. He wants to buy the most fuel efficient one.

Complete the table.

Car	Litres used	Distance travelled (km)	L/km
$Magnum$	$13.405$13.405	$38.3$38.3	$\editable{}$
$Falcador$	$20.71$20.71	$54.5$54.5	$\editable{}$
$Canyonero$	$6.336$6.336	$19.2$19.2	$\editable{}$
$Civil$	$2.754$2.754	$8.1$8.1	$\editable{}$

Which car is the most fuel efficient?
$Civil$
A
$Magnum$
B
$Canyonero$
C
$Falcador$
D

Question 3

$James$ paid $\$89$$89 for $61$61 L of petrol in $North Haverbrook$ . $Valentina$ paid $\$76$$76 for $45$45 L of petrol in $Dunkilderry$ .

How much does petrol cost per litre in $North Haverbrook$ ? Give your answer correct to the nearest $cent$ .
How much does petrol cost per litre in $Dunkilderry$ ? Give your answer correct to the nearest $cent$ .
In which suburb is petrol cheaper?
$North Haverbrook$
A
$Dunkilderry$
B
$James$ pumps $28$28 L in $Oklachusetts$ . Using your answers from parts (a) and (b), how much will this cost if the petrol price matches the best price between $North Haverbrook$ and $Dunkilderry$ ?

Outcomes

MS2-12-3

interprets the results of measurements and calculations and makes judgements about their reasonableness, including the degree of accuracy and the conversion of units where appropriate

4.02 Comparing rates