Aussie Maths & Science Teachers: Save your time with SmarterEd
Clara is comparing the costs of two different ways of travelling to work.
Clara’s motor scooter uses one litre of fuel for every 22 km travelled. The cost of fuel is $2.24/L and the distance from her home to the work car park is 33 km. The cost of travelling by bus and light rail is $35.80 for 10 single trips.
Which way of travelling is cheaper and by how much? Support your answer with calculations. (2 marks)
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\(\text{Motor scooter is }$0.22 \text{ cheaper per one-way trip.}\)
\(\text{Compare cost of a one-way trip}\)
\(\text{Motor scooter}\)
\(\text{Fuel used}=\dfrac{33}{22}=1.5\ \text{L}\)
\(\text{Cost}=1.5\times 2.24=$3.36\)
\(\text{Bus and light rail}\)
\(\text{Cost}=\dfrac{35.80}{10}=$3.58\)
\(\text{Difference}=$3.58-3.36=$0.22\)
\(\therefore\ \text{Motor scooter is }$0.22 \text{ cheaper per one-way trip.}\)
Lisa’s motorbike uses fuel at the rate of 1.8 L per 100 km for long-distance driving and 2.3 L per 100 km for short-distance driving.
She used the motorbike to make a journey of 840 km, which included 108 km of short-distance driving.
Approximately how much fuel did Lisa’s motorbike use on the journey?
\(B\)
\(\text{Fuel used in short distance}\)
\(=\dfrac{108}{100}\times 2.3\ \text{L}=2.484\ \text{L}\)
\(\text{Fuel used in long distance}\)
\(=\dfrac{840-108}{100}\times 1.8\ \text{L}=13.176\ \text{L}\)
| \(\therefore\ \text{Total Fuel}\) | \(=2.484+13.176\) |
| \(=15.66\ \text{L}\) |
\(\Rightarrow B\)
Bonn’s car uses fuel at the rate of 6.1 L /100 km for country driving and 8.3 L /100 km for city driving. On a trip, he drives 350 km in the country and 40 km in the city.
Calculate the amount of fuel he used on this trip. (2 marks)
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\(24.67\ \text{L}\)
\(\text{Fuel used in country}\)
\(=350\times \dfrac{6.1}{100}\)
\(=21.35\ \text{L}\)
\(\text{Fuel used in city}\)
\(=40\times \dfrac{8.3}{100}\)
\(=3.32\ \text{L}\)
\(\therefore\ \text{Total fuel used}\)
\(=21.35+3.32\)
\(=24.67\ \text{L}\)
The driving distance from Burt's home to his work is 15 km. He drives to and from work five times each week. His car uses fuel at the rate of 12 L/100 km.
How much fuel does he use driving to and from work each week?
\(B\)
\(\text{Total distance travelled each week}\)
\(=5\times 2\times 15\)
\(=150\ \text{km}\)
\(\therefore\ \text{Total fuel used}\)
\(=\dfrac{150}{100}\times 12\ \text{L}\)
\(=18\ \text{L}\)
\(\Rightarrow B\)
Christopher is comparing two different models of 4WD cars. Car A uses fuel at the rate of 11.4 L/100 km. Car B uses 9.6 L/100 km.
Suppose Christopher plans on driving \(11\ 000\) km in the next year.
How much less fuel will he use driving car B instead of car A?
\(A\)
\(\text{Difference in fuel usage}\)
\(=(11.4-9.6)\ \text{L/100 km}\)
\(=(1.8\ \text{L/100 km}\)
\(\therefore\ \text{Fuel saved using car}\ B\)
\(=\dfrac{11\ 000}{100}\times 1.8\)
\(=198\ \text{L}\)
\(\Rightarrow A\)
A car travels 480 km on 37 L of petrol.
What is its fuel consumption, correct to 1 decimal place?
\(B\)
\(37\text{ litres are used to travel}\ 4.8\times 100\ \text{km}\)
\(\text{Fuel consumption (L/100 km)}\)
\(=\dfrac{37}{4.8}\)
\(=7.7083\dots\)
\(=7.7\ \text{L/100 km}\)
\(\Rightarrow B\)