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 compare different rates. This is really helpful in everyday life because we can determine which car is faster, which shop is offering a better deal and even which job pays more!
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 equivalent.
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 ie. 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.
Let's look through some more examples.
Worked Examples
Question 1
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
AMagnum
BCanyonero
CFalcador
D
Question 2
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
ADunkilderry
BJames 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?