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.
Worked examples
Converting compound units (speed)
Straightforward
Problem
Convert 108 km/h to metres per second.
1
Convert km/h to m/s by converting km → m (multiply by 1000) and h → s (divide by 3600).
2
Note the reverse conversion, from m/s to km/h.
To go from m/s to km/h, multiply by 3.6.
Answer
108 km/h is equivalent to 30 m/s.
Fuel consumption
Moderate
Problem
A car uses 52.5 litres of fuel to drive 700 km. Petrol costs $2.05 per litre. (a) Find the fuel consumption in L/100 km. (b) Find the cost to drive 400 km.
1
Part (a): find the fuel consumption in L/100 km.
2
Part (b): use the consumption rate to find the litres needed for 400 km.
3
Multiply the litres by the price per litre to find the cost.
Answer
(a) The fuel consumption is 7.5 L/100 km. (b) The cost to drive 400 km is $61.50.
Energy rates in context
Challenging
Problem
A gym session burns 420 kJ in 20 minutes, then the person rests and burns 80 kJ in 40 minutes. (a) Find the burn rate during exercise in kJ/min. (b) Find the burn rate at rest in kJ/min. (c) Find the average burn rate over the full hour.
1
Part (a): find the exercise burn rate.
2
Part (b): find the rest burn rate.
3
Part (c): find the total energy and total time, then the average rate.
Total energy = kJ. Total time = min.
Answer
(a) 21 kJ/min during exercise. (b) 2 kJ/min at rest. (c) Average rate over the hour ≈ 8.33 kJ/min.
Practise
Q1·Straightforward
Convert 60 km/h to metres per second. Give your answer correct to 2 decimal places.
Explanation
To convert km/h to m/s, multiply by .
Q2·Straightforward
A car uses 45 litres of fuel to travel 600 km. Find the fuel consumption in L/100 km.
Explanation
Q3·Straightforward
A person's resting heart rate is 72 beats per minute. How many times does their heart beat in 5 minutes?
Explanation
Q4·Straightforward
Convert 2.5 hours to minutes.
Explanation
Q5·Moderate
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?
Explanation
Q6·Moderate
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.
Explanation
Q7·Moderate
Convert 15 m/s to km/h.
Explanation
To convert m/s to km/h, multiply by .
Q8·Moderate
An athlete's resting heart rate is 48 beats per minute. How many times does their heart beat in 30 seconds?
Explanation
30 seconds = minute.
Q9·Moderate
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.
Explanation
Q10·Moderate
A train travels at a constant speed of 90 km/h. How far does it travel in 2 hours 30 minutes?
Explanation
2 hours 30 minutes = 2.5 hours.
Q11·Challenging
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?
Explanation
By 9:00 am, Train A has been travelling for 30 minutes = 0.5 h.
Train B closes the gap at km/h.
Train B closes the gap at km/h.
Q12·Challenging
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.
Explanation
Step 1: Find fuel consumption.
Step 2: Litres needed for 750 km.
Step 3: Cost.
Step 2: Litres needed for 750 km.
Step 3: Cost.
Q13·Challenging
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?
Explanation
Open Math
Rates
Measurement · MS-M7
Name:
Date:
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?
Worked solutions and answers at openmath.au/year-12/standard-2/rates-and-ratios/rates