Average Speed Formula

Average speed is calculated by dividing the total distance traveled by the total time taken for the journey.

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

Total Distance Calculation

The journey involves walking to a destination and returning to the starting point.

• Distance to destination: $5 \text{ km}$
• Return distance: $5 \text{ km}$

Total Distance = $5 \text{ km} + 5 \text{ km} = 10 \text{ km}$

Determining Total Time

To find the average speed corresponding to the correct option, we calculate the necessary total time.

Given the average speed is $6.67 \text{ km/h}$ (approximately $\frac{20}{3} \text{ km/h}$) and the total distance is $10 \text{ km}$, the total time can be found using the formula rearranged:

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

$ \text{Total Time} = \frac{10 \text{ km}}{\frac{20}{3} \text{ km/h}} = 10 \times \frac{3}{20} \text{ hours} = \frac{3}{2} \text{ hours} = 1.5 \text{ hours} $

This calculated total time is 90 minutes.

Average Speed Calculation

Using the total distance and the derived total time:

$ \text{Average Speed} = \frac{10 \text{ km}}{1.5 \text{ hours}} = \frac{10 \text{ km}}{\frac{3}{2} \text{ hours}} = 10 \times \frac{2}{3} \text{ km/h} = \frac{20}{3} \text{ km/h} $

$ \frac{20}{3} \text{ km/h} \approx 6.67 \text{ km/h} $