Speed, Distance, and Time

Understanding the Relationship

In mathematics, speed, distance, and time are related through a simple formula. This formula helps us calculate one of these quantities if we know the other two.

The formula is:

$$\text{Speed} = \frac{\text{Distance}}{\text{Time}}$$

This can be rearranged to find distance or time:

• Distance: $$\text{Distance} = \text{Speed} \times \text{Time}$$
• Time: $$\text{Time} = \frac{\text{Distance}}{\text{Speed}}$$

Units of Measurement

• Speed is usually measured in kilometers per hour (km/h) or meters per second (m/s).
• Distance is measured in kilometers (km) or meters (m).
• Time is measured in hours (h), minutes (min), or seconds (s).

 

Worked Example

 

Examples

Example 1: Calculating Distance

If a train travels at a speed of 80 km/h for 2.5 hours, how far does it travel?

• Use the formula: $$\text{Distance} = \text{Speed} \times \text{Time}$$
• Substitute the known values: $$\text{Distance} = 80 \text{ km/h} \times 2.5 \text{ h} = 200 \text{ km}$$
• The train travels 200 km.

 

Example 2: Calculating Time

A cyclist covers a distance of 90 km at a speed of 30 km/h. How long does it take?

• Use the formula: $$\text{Time} = \frac{\text{Distance}}{\text{Speed}}$$
• Substitute the known values: $$\text{Time} = \frac{90 \text{ km}}{30 \text{ km/h}} = 3 \text{ h}$$
• It takes the cyclist 3 hours.