Fuel Consumption
Learn about fuel consumption for NSW Year 12 Mathematics Standard 1 (NESA outcome MST-12-S1-05). Fuel consumption is a rate in litres per 100 kilometres (L/100 km) — a car rated at 7 L/100 km burns 7 litres of fuel for every 100 km it drives.
You will find the fuel used on a trip, calculate a vehicle's fuel consumption rate, work out the cost of fuel, and use these rates to see which car is more fuel-efficient — the lower rate wins, which matters when buying a car or planning a road trip.
Theory
Fuel consumption is a rate that tells you how many litres a vehicle uses to travel \(100\text{ km}\), written L/100 km. This Year 12 Standard 1 (NSW) guide shows how to find the fuel used on a trip, the consumption rate, the cost of petrol, and which vehicle is more fuel-efficient.
Fuel consumption is a rate measured in litres per 100 kilometres (L/100 km). A car rated at \(7\) L/100 km uses \(7\) litres of fuel for every \(100\text{ km}\) it travels.
To find the fuel used, divide the distance by \(100\) to count the lots of \(100\text{ km}\), then multiply by the rate. To find the rate, divide the litres used by the distance and multiply by \(100\). The cost of fuel \(=\) litres used \(\times\) price per litre.
When comparing vehicles, write each rate in L/100 km. The lower rate is the more fuel-efficient vehicle and costs less to run. This is a core Year 12 Standard 1 (NSW) Ratios and rates skill.
Fuel used on a trip:
Fuel consumption rate in L/100 km:
Cost of the fuel:
How to solve a fuel consumption problem
- Identify what you know: the rate (L/100 km), the distance, the litres used or the price per litre.
- Fuel used: divide the distance by \(100\), then multiply by the rate.
- Rate: divide the litres by the distance, then multiply by \(100\).
- Cost: multiply the litres used by the price per litre, and round to the nearest cent.
Fuel used \(=\) rate \(\times\) the number of \(100\text{ km}\) travelled.
| \(\text{fuel}\) | \(=\) | \(\text{rate} \times \dfrac{\text{distance}}{100}\) |
| \(\) | \(=\) | \(6.5 \times \dfrac{420}{100}\) |
| \(\) | \(=\) | \(6.5 \times 4.2\) |
| \(\therefore\ \text{fuel}\) | \(=\) | \(27.3\text{ L}\) |
The hatchback uses \(27.3\) litres.
Litres used \(\div\) distance, then \(\times 100\).
| \(\text{rate}\) | \(=\) | \(\dfrac{52}{400} \times 100\) |
| \(\) | \(=\) | \(0.13 \times 100\) |
| \(\therefore\ \text{rate}\) | \(=\) | \(13\text{ L/100 km}\) |
The four-wheel drive uses \(13\) L/100 km.
Find the litres used, then multiply by the price per litre.
| \(\text{fuel}\) | \(=\) | \(9 \times \dfrac{380}{100}\) |
| \(\) | \(=\) | \(9 \times 3.8 = 34.2\text{ L}\) |
| \(\text{cost}\) | \(=\) | \(34.2 \times \$1.95\) |
| \(\therefore\ \text{cost}\) | \(=\) | \(\$66.69\) |
The petrol costs \(\$66.69\).
Write both as L/100 km, then cost the same trip.
| \(\text{(i) Car X}\) | \(=\) | \(\dfrac{38.5}{550} \times 100 = 7\text{ L/100 km}\) |
| \(7\) | \(\lt\) | \(7.5 \ \Rightarrow\ \text{Car X}\) |
| \(\text{(ii) X}\) | \(=\) | \(7 \times \dfrac{800}{100} = 7 \times 8 = 56\text{ L}\) |
| \(\text{Y}\) | \(=\) | \(7.5 \times \dfrac{800}{100} = 7.5 \times 8 = 60\text{ L}\) |
| \(\text{saving}\) | \(=\) | \((60 - 56) \times \$1.88\) |
| \(\therefore\ \text{saving}\) | \(=\) | \(4 \times \$1.88 = \$7.52\) |
(i) Car X; (ii) its petrol is \(\$7.52\) cheaper.
Common pitfalls
Frequently asked questions
What does L/100 km mean?
L/100 km is the number of litres of fuel a vehicle uses to travel 100 kilometres. A car rated at 6.5 L/100 km uses 6.5 litres for every 100 km it drives.
How do you calculate fuel used for a trip?
Divide the distance by 100 to find how many lots of 100 km there are, then multiply by the fuel consumption rate. A car using 6.5 L/100 km on a 420 km trip uses 6.5 times 4.2, which is 27.3 litres.
How do you calculate fuel consumption in L/100 km?
Divide the litres used by the distance travelled, then multiply by 100. A four-wheel drive that uses 52 litres to travel 400 km has a rate of 52 divided by 400 times 100, which is 13 L/100 km.
How do you work out the cost of fuel for a trip?
Work out the litres used, then multiply by the price per litre. A ute using 34.2 litres with petrol at $1.95 per litre costs 34.2 times 1.95, which is $66.69.
Is a higher or lower L/100 km better?
Lower is better. A lower number means the vehicle uses less fuel to travel the same distance, so it is more fuel-efficient and cheaper to run.