The driver of a car sees a person 80 metres ahead of him. The person is 120 metres behind after 40 seconds. If the speed of the car is $30 \mathrm{km}/\mathrm{h}$, find the speed of the person.

Speed is the ratio of distance travelled to time spent travelling. Because it has just one direction and no magnitude, speed is a scalar quantity.

Given:
The speed of the car: $30 \mathrm{km}/\mathrm{h}$
In the beginning, the person is 80 metres ahead of the car. After 40 seconds, the person is 120m behind the car.

Formula:
Speed =$\frac{\mathrm{Total} \mathrm{distance}}{\mathrm{Total} \mathrm{time}}$

Solution:

After 30 seconds, the total distance between them: $80 \mathrm{m} +120 \mathrm{m}= 200 \mathrm{m}$.

Now the relative speed = $\frac{\mathrm{Total} \mathrm{distance}}{\mathrm{Total} \mathrm{time}}$$=\frac{200}{40}=5 \mathrm{m}/\sec$

When we convert speed into $\mathrm{km}/\mathrm{h}$ from $\mathrm{m}/\sec$ we multiply by $\frac{5}{18}$.

Then the relative speed in $\mathrm{km}/\mathrm{h}= 5 \times \frac{18}{5}=18 \mathrm{km}/\mathrm{h}$

Now relative speed = Speed of the car - Speed of the person

$\Rightarrow 18= 30 - \mathrm{Speed} \mathrm{of} \mathrm{the} \mathrm{person}$

$\therefore$$\mathrm{Speed} \mathrm{of} \mathrm{the} \mathrm{person} = 12 \mathrm{km}/\mathrm{h}$