Fuel Consumption
Learn fuel consumption for NSW Year 12 Mathematics Standard 2. Fuel consumption is a rate measured in litres per 100 km (L/100 km) — the amount of petrol a car uses to travel 100 kilometres, and a key everyday example of the rates you study in Standard 2.
You will calculate a car's consumption rate, work out the fuel used and the cost of the petrol for a trip, and compare two vehicles to decide which is cheaper to run — practical Standard 2 skills for budgeting a real road trip.
Theory
Fuel consumption is a rate in the Year 12 Standard 2 (NSW) rates topic, measured in litres per 100 km. This guide shows how to find a car's consumption rate, calculate the fuel used on a trip, work out the fuel cost, and compare two vehicles to see which is cheaper to run.
Fuel consumption is a rate that tells you how thirsty a vehicle is. In Australia it is quoted in litres per 100 km (L/100 km): the number of litres of petrol the car uses to travel 100 km.
You find the rate by dividing the litres used by the distance travelled and scaling to 100 km: \(\text{consumption}=\dfrac{\text{litres used}}{\text{distance}}\times100\). Once you know the rate you can turn it around to find the fuel used for any trip, and then the fuel cost.
In this Year 12 Standard 2 (NSW) topic fuel consumption is one of the rates you work with: fuel used \(=\) rate \(\times\dfrac{\text{distance}}{100}\), fuel cost \(=\) fuel used \(\times\) price per litre, and you compare vehicles by which uses less fuel over the same distance.
Fuel consumption is a rate in litres per 100 km:
Rearranged, the fuel used on a trip of distance \(d\) km at rate \(r\) L/100 km is:
The fuel cost multiplies the litres used by the price per litre \(p\):
How to solve a fuel-consumption problem
- Identify the consumption rate \(r\) (L/100 km), the distance \(d\) (km) and the petrol price \(p\) (\$/L) from the question.
- Rate: if it is unknown, divide the litres used by the distance and \(\times100\).
- Fuel used: multiply the rate by \(\dfrac{d}{100}\) — divide the distance by 100 first because the rate is per 100 km.
- Cost or compare: multiply the litres used by the price per litre for the cost, or compare two cars' fuel (or cost) over the same trip — the smaller value wins.
Divide the litres used by the distance, then scale to 100 km.
| \(\text{consumption}\) | \(=\) | \(\dfrac{\text{litres used}}{\text{distance}}\times100\) |
| \(\) | \(=\) | \(\dfrac{46.2}{550}\times100\) |
| \(\) | \(=\) | \(0.084\times100 = 8.4\) |
The car uses \(8.4\) L/100 km.
Multiply the rate by the distance divided by 100.
| \(\text{fuel used}\) | \(=\) | \(r\times\dfrac{d}{100}\) |
| \(\) | \(=\) | \(9.5\times\dfrac{340}{100}\) |
| \(\) | \(=\) | \(9.5\times3.4 = 32.3\) |
The ute uses \(32.3\) litres.
Find the litres used, then multiply by the price per litre.
| \(\text{fuel used}\) | \(=\) | \(7.5\times\dfrac{480}{100} = 36\text{ L}\) |
| \(\text{cost}\) | \(=\) | \(36\times\$1.92\) |
| \(\) | \(=\) | \(\$69.12\) |
The trip costs \(\$69.12\) in petrol.
Cost each car's fuel for the same trip, then subtract.
| \(\text{Car A}\) | \(=\) | \(6.8\times6\times\$1.85 = \$75.48\) |
| \(\text{Car B}\) | \(=\) | \(8.5\times6\times\$1.85 = \$94.35\) |
| \(\text{saving}\) | \(=\) | \(\$94.35-\$75.48 = \$18.87\) |
Car A is cheaper to run, by \(\$18.87\) over the \(600\) km trip.
Common pitfalls
Frequently asked questions
What does fuel consumption in L/100 km mean?
It is the number of litres of petrol a vehicle uses to travel 100 kilometres. For example, 8 L/100 km means the car burns 8 litres of petrol every 100 km. A lower number means the car is more economical.
How do you calculate fuel consumption?
Divide the litres of petrol used by the distance travelled, then multiply by 100. For example, a car that uses 46.2 litres over 550 km has a consumption of 46.2 divided by 550, times 100, which is 8.4 L/100 km.
How do you work out the fuel used for a trip?
Multiply the consumption rate by the trip distance divided by 100, because the rate is per 100 km. A car at 9.5 L/100 km on a 340 km trip uses 9.5 times 3.4, which is 32.3 litres.
How do you find the cost of petrol for a trip?
First work out the litres of fuel used, then multiply by the price per litre. If a trip uses 36 litres and petrol is $1.92 per litre, the cost is 36 times 1.92, which is $69.12.
Is a higher or lower L/100 km better?
Lower is better. A smaller L/100 km figure means the car uses less petrol to cover the same distance, so it is more economical and cheaper to run. This is the opposite of a speed, where a bigger number is faster.
How do you compare two cars' fuel use?
Work out the fuel used (or the fuel cost) for each car over the same distance, then compare. The car with the smaller consumption rate always uses less fuel and costs less to run over any given trip.