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9.04 The cost of fuel

Worksheet
Fuel consumption rate
1

Calculate the fuel consumption (\text{L/100 km}) of a car that travels 270 \text{ km} on 80 \text{ L}. Round your answer to two decimal places.

2

On a certain Monday, unleaded fuel is priced at 114.9 cents per litre. Calculate the cost of a full tank of fuel for the following fuel tank capacities:

a

56 \text{ L}

b

64 \text{ L}

c

71 \text{ L}

d

87 \text{ L}

3

Luke drives a 6-cylinder Ford Falcon. Its fuel consumption when driving in urban environments is 8.8 \text{ L/100 km}. Calculate the exact amount of fuel consumed for the following distances he travelled:

a

70 \text{ km}

b

120 \text{ km}

4

Luke drives a 6-cylinder Ford Falcon. Its fuel consumption when driving in urban environments is 10 \text{ L/100 km}. Calculate the amount of fuel consumed for the following distances he travelled, correct to three decimal places:

a

9 \text{ km}

b

12 \text{ km}

c

17 \text{ km}

d

24 \text{ km}

5

The fuel consumption rates of six cars is given in the table below:

\text{Car Model}\text{Fuel Type}\text{Economy (L/100 km)}
\text{Mazda 3}\text{Diesel}5.1
\text{BMW 118d}\text{Diesel}4.3
\text{Volkswagon Polo GTI}\text{Petrol}5.7
\text{Ford Focus}\text{Petrol}5.8
\text{Toyota Prius}\text{Hybrid}3.9
\text{Honda Civic}\text{Hybrid}4.6

How far can the BMW 118d travel on a tank of 63 \text{ L}? Round your answer to the nearest kilometre.

6

Yvonne's car has a fuel consumption rate of 8 \text{ L/100 km}. Her car's fuel tank can hold 65 \text{ L} of petrol.

a

How far can the car travel on 1 \text{ L} of petrol?

b

Yvonne is driving on the freeway and notices that her fuel tank is \dfrac{1}{4} full. How much further can she drive on the amount of fuel she has remaining?

7

A Lamborgotti Fasterossa has a fuel consumption of 10.4 \text{ L/100 km}.

a

Find the exact fuel consumption in \text{L/km}.

b

How much fuel does it use to travel 790 \text{ km}? Round your answer to the nearest litre.

c

How far could it travel on a 55 \text{ L} tank of fuel? Round your answer to the nearest kilometre.

d

If the Lamborgotti used 66 \text{ L} to go 885 \text{ km}, how far could it go on 139 \text{ L} at the same rate? Round your answer to the nearest kilometre.

8

Sarah drove 422 \text{ km} from Location A to Location B. She filled up her 50 \text{ L} tank in Location A, and after 382 \text{ km} of driving on the freeway, her tank was \dfrac{1}{4} full. The last 40 \text{ km} of the journey, she drove through the city. By the time she got to Location B, she had 7.5 \text{ L} left.

a

Complete the given table:

\text{Distance travelled (km)}\text{Fuel consumed (L)}
Freeway
Through city
b

By how much was her rate of fuel consumption on the freeway lower than her fuel consumption driving through the city? Give your answer in \text{L/100 km} and correct to two decimal places.

Compare fuel consumption
9

In one year, a small car running on unleaded fuel travels a total of 11\,500 \text{ km} and has a fuel consumption of 7.5 \text{ L/100 km}. In contrast, a larger car running on diesel fuel travels 15\,000 \text{ km} and has a fuel consumption of 10.2 \text{ L/100 km}. The average cost of unleaded fuel is \$1.43 per litre, and the average cost of diesel fuel is \$1.43 per litre. Calculate:

a

The total annual cost of fuel for the small car, correct to two decimal places.

b

The total annual cost of fuel for the large car, correct to two decimal places.

c

The distance the large car would need to have travelled (to the nearest kilometre) such that its annual cost of fuel is \$2090.

10

Frank and Bart both own the same make and model of car. The fuel consumption data for their vehicle is listed in the following table:

  • Frank lives in outback NSW where the average price of petrol is 143.7 \text{c} per litre and estimates his fuel costs using the extra urban fuel consumption rate.

  • Bart lives in Sydney where the average price of petrol is 121.9\text{c} per litre and estimates his fuel costs using the urban fuel consumption rate.

\text{Consumption Type}\text{Consumption rate} \\ \text{(L per 100 km)}
\text{Urban}9.5
\text{Combined}7.2
\text{Extra urban}5.5
a

Frank travels 350 \text{ km} per week in the car, every week of the year. Calculate how much Frank pays for petrol each week.

b

Bart also travels 350 \text{ km} per week in the car, every week of the year. Calculate how much Bart pays for petrol each week.

c

Calculate the difference in fuel costs over the entire year. Assume that there are 52 weeks in a year.

11

Dave compares the fuel consumption rates of two similar 2018 model Holden Commodores. One has a 4-cylinder engine while the other has a 6-cylinder engine. Both are automatic sedans with the same fuel tank capacity of 61 \text{ L}.

The given table shows fuel consumption rate in litres per 100 \text{ km}.

\text{4-cylinder}\text{6-cylinder}
Combined7.88.8
Urban9.512
Extra urban6.27.1
a

If the price of fuel is 122.9\text{c} per litre, what is the cost of completely filling the tank for each car?

b

Using the extra urban fuel consumption rate, work out how far each car can travel on a full tank of fuel. Round your answers to the nearest kilometre.

i

4-cylinder

ii

6-cylinder

c

If Dave drives 19\,000 \text{ km} per year and the average price of fuel is 122.9\text{c} per litre, calculate the annual cost of fuel for each vehicle. Use the combined fuel consumption rate in your calculations. Round your answer to the nearest dollar.

i

4-cylinder

ii

6-cylinder

12

The following table outlines the \text{CO}_2 emissions rates for a 2018 model sedan. The car can be purchased with either a 4-cylinder engine or a 6-cylinder engine.

\text{Purchase price}\text{Engine size}\text{CO}_2 \text{ emissions (g/km)}
\$38\,980\text{4-cylinder}163
\$42\,430\text{6-cylinder}196
a

As a way of reducing the environmental impact of greenhouse gases, the state government is considering a new stamp duty based on the \text{CO}_2 emissions of the vehicle as shown below:

\text{CO}_2 \text{ emissions}\text{Stamp duty payable}
141 - 190 \text{ g/km}3.15 \%
191 - 225 \text{ g/km}4.45 \%

Calculate the stamp duty that must be paid to register both the 4-cylinder and 6-cylinder vehicle. Round your answer to the nearest dollar.

i

4-cylinder

ii

6-cylinder

b

If both vehicles travelled 23\,500 \text{ km} in a year, how many kilograms of \text{CO}_2 would be saved by driving the 4-cylinder vehicle as opposed to the 6-cylinder vehicle?

13

A car company wanted to know about the efficiency of a certain model of car. Their results were gathered in the table below:

\text{Distance travelled}\text{Fuel consumed}
100 \text{ km/hr with no additional tow}141 \text{ km}17 \text{ L}
80 \text{ km/hr with no additional tow}43 \text{ km}4 \text{ L}
100 \text{ km/hr towing } 1 \text{ tonne}130 \text{ km}20 \text{ L}
a

Driving at 100 \text{ km/hr}, how much greater is the rate of fuel consumption than at \\ 80 \text{ km/hr}? Leave your answer in \text{L/100 km} and correct to two decimal places.

b

What is the increase in fuel consumption per 100 \text{ km} for a car to travel at 100 \text{ km/hr}, towing 1 tonne, than it is for a car to travel at 100 \text{ km/hr} without any additional weight? Leave your answer in \text{L/100 km} and correct to two decimal places.

Cost of fuel
14

A V6 car consumes 11.3 \text{ L/100 km} and runs on unleaded fuel.

a

How much fuel will be required for a 90 \text{ km} trip? Round your answer to two decimal places.

b

Calculate the cost for a 90 \text{ km} trip.

Petrol typePrice (cents per litre)
\text{Unleaded}136
\text{Diesel}164.6
\text{E10 Unleaded}134.6
15

Consider the following table:

a

A V6 car consumes 13 \text{ L/100 km} and runs on unleaded fuel. Calculate the cost for a 60 \text{ km} trip.

b

A 4-cylinder car consumes 8.7 \text{ L/100 km} and runs on E10 Unleaded. Calculate the cost for a 80 \text{ km} trip.

c

A V8 car consumes 14.5 \text{ L/100 km} and runs on diesel fuel. Calculate the cost of a 70 \text{ km} trip.

Petrol typePrice (cents per litre)
\text{Unleaded}120.9
\text{Diesel}164.1
\text{E10 Unleaded}114.7
16

Paul lives in a city and wants to compare the costs of getting to and from work each day. If he goes by train it will cost him \$8.80 per day and if he travels by bus it will cost him \$9.60 per day. Paul travels to and from work, five days a week for 48 weeks of the year.

a

How many days each year does Paul spend travelling to and from work?

b

Calculate his annual transport cost if he travels by:

i

Train

ii

Bus

c

Paul decides to buy a new car with an urban fuel consumption rate of 7.5 \text{ L/100 km}. The total driving distance to and from work is 32 \text{ km}. The average price of fuel is 123 cents per litre. Calculate Paul's fuel cost for driving to and from work, for one day.

d

Calculate Paul's annual fuel cost for driving to and from work.

e

Paul's total car expenses for the year, including registration, insurance, service, depreciation and fuel costs come to \$8700. Paul estimates that he uses his car 43\% of the time for getting to and from work. Calculate Paul's expense for getting to and from work using his car.

f

Which mode of transport is cheapest for Paul to get to and from work: car, bus, or train?

17

The fuel consumption of six cars is given in the table below:

\text{Car Model}\text{Fuel Type}\text{Economy (L/} 100 \text{km)}
\text{Mazda 3}\text{Diesel}5.1
\text{BMW 118d}\text{Diesel}4.3
\text{Volkswagon Polo GTI}\text{Petrol}5.7
\text{Ford Focus}\text{Petrol}5.8
\text{Toyota Prius}\text{Hybrid}3.9
\text{Honda Civic}\text{Hybrid}4.6
a

A family wanted to go on a road trip that would cover 2372 \text{ km} in their Honda Civic. How much fuel is needed for this trip? Round your answer up to the nearest litre to ensure enough fuel for the trip.

b

If the price of fuel is \$1.37 per litre, what is the cost of the fuel needed for this trip?

c

If the car has a tank size of 64 \text{ L}, how far in to the trip will it need to be refuelled? Round your answer to the nearest kilometre.

18

The prices of unleaded petrol, in cents per litre, for three different locations are given below:

MonTueWedThuFriSatSun
Perth125.6133.2122.7142.1140.2133.3123.8
Canberra149.9119.5144.3113.3134.2131.4128.8
Sydney146.7124.8114.6130.2121.9120142.2
a

Calculate the daily average petrol price for Sydney. Round your answer to two decimal places.

b

In Canberra, what is the difference in price for filling a 50 \text{ L} tank on Monday compared to on Sunday?

c

Tom filled his tank of petrol in Canberra on Sunday. If his rate of fuel consumption is 9.7 \text{ L/100 km} and his car travelled 515 \text{ km} on the one tank, what was the cost to fill his car with petrol?

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models relevant financial situations using appropriate tools

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