Rates and ratios

Convert between units and compound units; solve problems involving rates (fuel consumption, heart rate, energy, speed); divide quantities in a given ratio; apply scale factors to lengths, areas and volumes of similar figures.

Measurement · MS-M7

Sub-topics

Rates

Convert between units and compound units; solve real-world problems involving fuel consumption (L/100 km), heart rate, energy (kJ/Cal), speed and average rates.

Ratios and scale

Divide quantities in a given ratio; interpret and use scale drawings, maps and plans; apply the scale factor relationships

k : k^2 : k^3

for lengths, areas and volumes of similar figures.

Open Math

Rates and ratios

Measurement · MS-M7

Name:

Date:

Rates

Q1Straightforward

Convert 60 km/h to metres per second. Give your answer correct to 2 decimal places.

Q2Straightforward

A car uses 45 litres of fuel to travel 600 km. Find the fuel consumption in L/100 km.

Q3Straightforward

A person's resting heart rate is 72 beats per minute. How many times does their heart beat in 5 minutes?

Q4Straightforward

Convert 2.5 hours to minutes.

Q5Moderate

A car has a fuel consumption of 8.4 L/100 km. How many litres of fuel does it need for a 350 km trip?

Q6Moderate

One food Calorie (Cal) is approximately 4.184 kJ. How many kilojoules are in a meal containing 250 Cal? Give your answer to the nearest whole number.

Q7Moderate

Convert 15 m/s to km/h.

Q8Moderate

An athlete's resting heart rate is 48 beats per minute. How many times does their heart beat in 30 seconds?

Q9Moderate

A runner burns 650 kJ during a 30-minute training session. What is their average energy burn rate in kJ per minute? Give your answer correct to 2 decimal places.

Q10Moderate

A train travels at a constant speed of 90 km/h. How far does it travel in 2 hours 30 minutes?

Q11Challenging

Train A departs at 8:30 am travelling at 110 km/h. Train B departs from the same station at 9:00 am on a parallel track, travelling at 130 km/h in the same direction. How many minutes after Train B departs will it catch Train A?

Q12Challenging

A car can travel 480 km on a full 40-litre tank of fuel. Fuel costs $2.10 per litre. How much does it cost in fuel to drive 750 km? Give your answer to the nearest cent.

Q13Challenging

A meal contains 2100 kJ of energy. Running burns energy at a rate of 35 kJ per minute. How many minutes would it take to burn off the entire meal through running?

Ratios and scale

Q14Straightforward

Divide $240 between Ali and Ben in the ratio

3:5

. How much does Ali receive?

Q15Straightforward

A map has a scale of

1:50\,000

. A river is 4 cm long on the map. What is the actual length of the river in kilometres?

Q16Straightforward

A scale drawing uses a scale of

1:20

. A room wall is 8 m long in real life. How long is the wall on the drawing, in centimetres?

Q17Moderate

A concrete mix uses cement, sand and gravel in the ratio

1:2:4

. If 70 kg of gravel is used, how many kilograms of cement are needed?

Q18Moderate

A map has a scale of

1:250\,000

. Two towns are 7.5 cm apart on the map. Find the actual distance between the towns in kilometres.

Q19Moderate

Two similar triangles have bases of 6 cm and 9 cm. The smaller triangle has an area of 18 cm². Find the area of the larger triangle in cm².

Q20Moderate

Divide 180 kg in the ratio

2:3:4

. What is the largest share, in kg?

Q21Moderate

Two similar boxes have lengths of 5 cm and 20 cm. The smaller box has a volume of 50 cm³. Find the volume of the larger box in cm³.

Q22Challenging

A map has a scale of

1:500\,000

. The driving distance between two cities is 120 km. What is this distance on the map, in centimetres?

Q23Challenging

A scale model of a car is built to a scale of

1:25

. The model is 6 cm high. What is the actual height of the car in metres?

Q24Challenging

Three people share profits in the ratio

5:3:2

. The largest share is $4500 more than the smallest share. Find the total profit in dollars.

Q25Challenging

Two similar cylinders have heights of 2 cm and 5 cm. The smaller cylinder has a volume of 80 cm³. Find the volume of the larger cylinder in cm³.

Worked solutions and answers at openmath.au/year-12/standard-2/rates-and-ratios