Compound measures
Compound measures involve two or more different units. Examples of compound measures and their units include speed (km/h), heart rate (beats per minute), miles per gallon (mpg).
Units for measuring such as metres, kilograms and litres are covered in the guide on metric units and are examples of single units.
Speed
The speed of an object is the distance covered in a period of time. Examples of speed units are metres per second (m/s), kilometres per hour (km/h) and miles per hour (mph).
If a car is travelling at a speed of 32 mph that means it will cover a distance of 32 miles in one hour.
A bird flying at 14 m/s will travel 14 metres in each second.
Calculating speed given distance and time
Average speed is calculated by dividing the total distance covered by the total time taken.
\(Speed = \frac{Distance}{Time}\) Or \(S = \frac{D}{T}\)
This triangle can be helpful for remembering the formula.
Example
Isla ran 200 metres in 31.25 seconds. What is her average speed?
\(Speed = \frac{Distance}{Time}\)
\(Speed = \frac{200}{31.25} = 6.4 m/s\)
Question
A plane travelled 4000 km in 5h 30 min. Calculate the average speed of the plane.
Distance = 4000 km
Time = 5 h 30 min = 5.5 h
\(Speed = \frac{Distance}{Time} = \frac{4000}{5.5} = 727.27 …\)
\(Speed = 727 km/h\) (correct to the nearest km/h)
Calculating distance given speed and time
If the speed and time are known, the formula can be rearranged to calculate distance by multiplying both sides by time.
\(\mathbf{Time} \color{black}\times Speed = \frac{Distance}{\cancel{Time}} \times \cancel{Time}}\)
Distance = Speed Ă— Time
D = S Ă— T
The triangle can help when rearranging the formula.
Example
Freddie cycled for 2 ½ hours with an average speed of 8 mph. How far did he cycle?
Speed = 8 mph
Time = 2 ½ h
Distance = Speed Ă— Time
Distance = 8 Ă— 2.5 = 20 miles
Question
The average speed of the train from Dublin to Belfast is 48 mph.
If the journey takes 2 hours and 15 minutes, estimate the distance between Dublin and Belfast.
Speed = 48 mph
Time = 2 h 15 min = 2.25 h
Distance = Speed Ă— Time
Distance = 48 Ă— 2.25 = 108
Distance = 108 miles
Calculating time given speed and distance
If the speed and distance are known the formula can be rearranged to calculate the time taken.
\(Time = \frac{Distance}{Speed}\)
\(T = \frac{D}{S}\)
The triangle can help when rearranging the formula.
Example
Kevin the caterpillar crawls at an average speed of 1.5 cm/s.
How long will it take Kevin to get to a lettuce patch which is 2.4 metres from him?
Speed = 1.5 cm/s
Distance = 2.4 metres = 240 cm
Note: Make sure the units match!
\(Time = \frac{Distance}{Speed}\)
\(Time = \frac{240}{1.5} = 160\)
Time = 160 s = 2 min 40 s
Question
Brent geese migrate from Greenland to Ireland for the winter, a distance of approximately 5040 km. The average speed including stops is 36 km/h. How many days will this flight take? Give your answer to the nearest day.
Distance = 5040 km
Speed = 36 km/h
\(Time = \frac{Distance}{Speed} = \frac{5040}{36} = 140 hours\)
140 ÷ 24 = 5.833 …
Time = 6 days
Calculations with other compound measures
Heart rate is the number of heart beats per minute.
Example
Poppy counted 24 beats in 20 seconds. What is her heart rate?
1 minute = 3 Ă— 20 seconds
Heart rate = 3 Ă— 24 = 72 beats per minute
A cars fuel economy is measured as the miles travelled per gallon of fuel.
Example
Hannah’s car display shows that the fuel economy is 42 mpg.
If the fuel tank holds 12 gallons how far can the car travel on one full tank of fuel?
The car can travel 42 miles for every gallon of fuel.
With 12 gallons of fuel the car can travel 12 Ă— 42 = 504 miles.
Test yourself
More on M1: Geometry and measures
Find out more by working through a topic
