smc-4609-55-Fuel consumption

Rates, SM-Bank 097

Caleb is travelling from Brisbane to Toowoomba. The journey is 135 kilometres.

His car uses 9.45 litres of fuel per 100 kilometres.

How much fuel will Caleb need to make the journey?

Round your answer to the nearest litre. (2 marks)

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$13\ \text{litres (nearest whole)}$

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$\text{Fuel needed}$	$=\dfrac{135}{100}\times 9.45$
	$= 12.75\dots$
	$= 13\ \text{litres (nearest whole)}$

Rates, SM-Bank 028

John's old tractor used 8.3 litres of fuel per 100km.

His new tractor uses 5.9 litres of fuel per 100 km.

John pays $2.15 per litre for fuel and drives 20,000 km each year.

How much money will John save on fuel each year with his new tractor? (2 marks)

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$$1032$

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$\text{Fuel cost of old tractor}$

$=8.3\times $2.15\times \dfrac{20\ 000}{100}$

$=8.3\times $2.15\times 200$

$=$3569$

$\text{Fuel cost of new tractor}$

$=5.9\times $2.15\times\dfrac{20\ 000}{100}$

$=5.9\times $2.15\times 200$

$=$2537$

$\therefore\ \text{John’s fuel savings each year}$

$=$3569-$2537$

$=$1032$

Rates, SM-Bank 026

Kurt is travelling from Newcastle to Sydney. The journey is 165 kilometres.

His car uses 8.35 litres of fuel per 100 kilometres.

How much fuel will Kurt need to make the journey?

Round your answer to the nearest litre. (2 marks)

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$14\ \text{litres (nearest whole number)}$

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$\text{Fuel needed}$	$=\dfrac{165}{100}\times 8.35$
	$= 13.77\dots$
	$= 14\ \text{litres (nearest whole number)}$

Rates, SM-Bank 020

Petrol costs 225.5 cents per litre.

How much, in dollars and cents, does 86 litres of petrol cost? (2 marks)

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$$193.93$

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$1\ \text{litre costs}\ 225.5\ \text {cents}=$2.255$

$\therefore\ 86\ \text{litres costs}$	$=86\times 2.255$
	$=$193.93$

Rates, SM-Bank 006

Pete travelled 646 kilometres and used 76 litres of fuel.

Express Pete's average fuel consumption in:

i. litres per 100 kilometres, giving your answer rounded to 1 decimal place. (2 marks)

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ii. kilometres per litre. (1 mark)

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If Pete's average fuel consumption remained the same, how many litres of fuel would he use to travel 272 kilometres? (2 marks)

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a. i. $11.8\ \text{L}/100\ \text{km (1 d.p.)}$

ii. $8.5\ \text{km}/\text{L}$

b. $32\ \text{litres}$

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a.	i. $\text{Average litres/100 km}$	$=\dfrac{76}{646}\times 100/100\ \text{km}$
		$=11.764\dots /100\ \text{km}$
		$\approx 11.8\ \text{L}/100\ \text{km (1 d.p.)}$

ii. $\text{Average km/L}$	$=\dfrac{646}{76}\ \text{km}/\text{L}$
	$=8.5\ \text{km}/\text{L}$

b.	$\text{Litres}$	$=\dfrac{272}{8.5}$
		$=32$

$\therefore\ \text{Pete would use}\ 32\ \text{litres of fuel to travel}\ 272\ \text{km.}$

\(\text{Fuel needed}\)	\(=\dfrac{135}{100}\times 9.45\)
	\(= 12.75\dots\)
	\(= 13\ \text{litres (nearest whole)}\)

\(\text{Fuel needed}\)	\(=\dfrac{165}{100}\times 8.35\)
	\(= 13.77\dots\)
	\(= 14\ \text{litres (nearest whole number)}\)

a.	i. \(\text{Average litres/100 km}\)	\(=\dfrac{76}{646}\times 100/100\ \text{km}\)
		\(=11.764\dots /100\ \text{km}\)
		\(\approx 11.8\ \text{L}/100\ \text{km (1 d.p.)}\)

b.	\(\text{Litres}\)	\(=\dfrac{272}{8.5}\)
		\(=32\)

\(\therefore\ 86\ \text{litres costs}\)	\(=86\times 2.255\)
	\(=$193.93\)

ii. \(\text{Average km/L}\)	\(=\dfrac{646}{76}\ \text{km}/\text{L}\)
	\(=8.5\ \text{km}/\text{L}\)