Compound measures are types of measure that involve two or more different units. Examples of compound measures include m/s, g/cm³, population per km² and miles per gallon.

Speed is calculated using the equation:

\[\text{speed}=\frac{\text{distance}}{\text{time}}\]

This is an example of a compound measure because distance and time can’t be measured in the same unit. Speed can be measured in metres per second, kilometres per hour and several other forms too.

Different measures have different sizes. 10 km/h is not the same as 10 m/s.

- Question
Calculate the average speed of a mongoose if it travels 4 km in 0.25 hours.

\[\text{speed}=\frac{\text{distance}}{\text{time}}\]

\[\text{speed}=\frac{\text{4~km}}{\text{0.25~hours}}\]

\[\text{speed = 16 km/h}\]

- Question
Calculate the average speed of a cheetah if it travels 300 m in 10 s.

\[\text{speed}=\frac{\text{distance}}{\text{time}}\]

\[\text{speed}=\frac{\text{300~m}}{\text{10~s}}\]

\[\text{speed = 30 m/s}\]

The equation for speed can also be rearranged into either of the following forms:

\[\text{distance}=\text{speed}\times{\text{time}}\]

or

\[\text{time}=\frac{\text{distance}}{\text{speed}}\]

This allows you to calculate either distance or time.

Distance and time are not compound measures as they are both measured in a single unit.

- Question
A car travels from Cardiff to London with an average speed of 50 mph. If the journey takes three hours, estimate the distance from Cardiff to London.

\[\text{distance}=\text{speed}\times{\text{time}}\]

\[\text{distance}=\text{50~mph}\times{\text{3~hours}}\]

\[\text{distance}=\text{150~miles}\]