A travels for 8 hours at the rate of 4 km/h and for 4 hours at the rate of 8 km/h. The average speed of the journey (in km/h) is:

To find the average speed of the entire journey, we use the formula for average speed:

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

Let's calculate the distance covered in each part of the journey:

First part of the journey:
A travels for 8 hours at a speed of 4 km/h.

${\mathrm{Distance}}_1=\text{Speed}\times \text{Time}=4\text{km/h}\times 8\text{h}=32\text{km}$

Second part of the journey:
A travels for 4 hours at a speed of 8 km/h.

${\mathrm{Distance}}_2=\text{Speed}\times \text{Time}=8\text{km/h}\times 4\text{h}=32\text{km}$

Total Journey Calculations:
Now, find the total distance and total time:

$\text{Total Distance}=32\text{km}+32\text{km}=64\text{km}$

$\text{Total Time}=8\text{h}+4\text{h}=12\text{hours}$

Calculating the Average Speed:
Substitute the total distance and total time back into the average speed formula:

$\text{Average Speed}=\frac{64}{12}=\frac{16}{3}\text{km/h}$

Converting the improper fraction to a mixed number:

$\frac{16}{3}=5\frac{1}{3}\text{km/h}$

Thus, the average speed of the journey is 5 1/3 km/h.