How much does a car cost? That is a surprisingly complicated question. They vary widely in price between different manufacturers, different models, and whether they're new or used. Cars also have different fuel efficiencies, there are many different kinds of fuel, and fuel costs change on a daily basis. In the same way as we did in 4.03 for homes, we are going to use rates to handle all of these considerations and work towards a simple answer.
Rate of fuel consumption, or fuel efficiency, describes the amount of fuel an engine uses over some measurement of distance. Usually the amount of fuel is given in litres and the distance is given in $100$100 kilometres, so the fuel consumption is then reported in L/$100$100 km. Advertised rates of fuel consumption for vehicles are assessed in standardised conditions so that different rates of fuel consumption can be directly compared between vehicles. These published rates are a useful starting point for comparison, but keep in mind that your personal rate of fuel consumption may be different - your use of the car may not reflect the terrain, speed, and loading of the car under test conditions.
The fuel economy of a car tells us something different - it describes how many kilometres a car can travel on one litre of fuel, which is reported in km/L. Fuel economy measures litres of fuel consumed over distance traveled, while rate of fuel consumption measures distance traveled over litres of fuel consumed. This inverse relationship means that as fuel economy increases, rate of fuel consumption decreases, and vice-versa.
Exploration
Say you were tossing up between purchasing two cars, Elite made by Horde, and Agile made by Folden. They are each advertised for $\$35000$$35000 from the showroom floor. Your research reveals that the Elite has a rate of fuel consumption of $5.5$5.5 L/$100$100 km, and the Agile has a fuel economy of $20$20 km/L. Using this information, which car will end up costing you the least in fuel?
We can convert between fuel economy and rate of fuel consumption, and we should do that first so we can compare the two models. We know the rate of fuel consumption of the Elite, and to find its fuel economy we first reciprocate the rate of fuel consumption - finding $1$1 over the rate - to tell us how many groups of $100$100 km the car can travel per litre. We then multiply this number by $100$100 to find out how many groups of $1$1 km the car can travel per litre, which is the fuel economy we were looking to find:
| Fuel economy of Elite | $=$= | $\frac{1}{5.5}\times100$15.5×100 km/L | (finding the reciprocal and multiplying by $100$100) |
| $=$= | $\frac{100}{5.5}$1005.5 km/L | (simplifying the multiplication) | |
| $\approx$≈ | $18$18 km/L | (converting into a decimal and rounding) |
So it turns out that the Agile has a better fuel economy (at $20$20 km/L) than the Elite.
Let's convert the other way just to be sure - we know the fuel economy of the Agile, and to find its rate of fuel consumption we first divide its fuel economy by $100$100. This tells us how many groups of $100$100 km the Agile can travel on a litre of fuel, and we then reciprocate this number to find its rate of fuel consumption:
| Rate of fuel consumption of Agile | $=$= | $\frac{1}{\frac{20}{100}}$120100 L/$100$100 km | (dividing by $100$100 and then reciprocating) |
| $=$= | $\frac{100}{20}$10020 L/$100$100 km | (simplifying the fraction) | |
| $=$= | $5$5 L/$100$100 km | (converting into a single number) |
As we expected, the rate of fuel consumption of the Agile is better than the Elite (because it is the lower number).
| Elite | Agile | |
|---|---|---|
| Fuel economy (km/L) | $18$18 | $20$20 |
| Rate of consumption (L/$100$100 km) | $5.5$5.5 | $5.0$5.0 |
To travel the coastline of NSW, which is about $2000$2000 km, the amount of fuel you would need for the Elite is $\frac{5.5\times2000}{100}=110$5.5×2000100=110 L, while the amount of fuel you would need for the Agile car is only $\frac{5.0\times2000}{100}=100$5.0×2000100=100 L.
You've almost made up your mind when you notice that they run on different kinds of fuel - Elite runs on petroleum while Agile runs on diesel. How will this affect your decision? You find out that the closest service station is selling petroleum for $135.2$135.2 cents per litre, and diesel for $157.3$157.3 cents per litre. Using this as a baseline, how much money does it cost to travel $2000$2000 km in each car? We can find this by multiplying the rate of consumption by the price (in dollars) of each fuel to find the price for $100$100 km, then multiplying this by $20$20 to find the price for $2000$2000 km.
For the Elite it would cost $5.5\times1.352\times20=\$148.72$5.5×1.352×20=$148.72 and for the Agile it would cost $5.0\times1.573=\$153.70$5.0×1.573=$153.70. If the price of petrol and diesel stays roughly the same, it ends up being more cost efficient to purchase the Elite in the long run.
Practice questions
question 1
A car travels $80$80 kilometres and consumes $6.96$6.96 litres of fuel.
What is the rate of fuel consumption of the car in L/km? Give your answer as a decimal.
What is the rate of fuel consumption of the car in L/$100$100 km?
question 2
Harry owns a 4WD with a fuel efficiency of $8$8 L/$100$100 km which requires $126$126 litres of fuel a week. Harry also owns a sedan which has a fuel efficiency of $7$7 L/$100$100 km which requires $240$240 litres of fuel.
What distance does the 4WD cover in a week?
What distance does the sedan cover in a week? Round your answer to two decimal places.
question 3
Amy has to travel $1450.4$1450.4 kilometres for a camping trip. Her car has a rate of fuel consumption of $8$8 km/L.
How much fuel is consumed on the trip? Give your answer in decimal form.
Amy's tank can hold $49$49 litres of fuel. How many times will she have to refuel? Your answer must be a whole number.