A man travels the first $200\text{km}$ of his journey at $80\text{km/hr}$. Due to bad weather he travels the next $200\text{km}$ of his journey at $50\text{km/hr}$. What is his average speed for the first $400\text{km}$ of his journey?

Since the distances covered in both intervals are equal ($d_1=d_2=200\text{km}$), the average speed can be computed directly using the harmonic mean formula:
$$\text{Average Speed}=\frac{2xy}{x+y}$$

Where:

* $x=80\text{km/hr}$ (speed of the first part)
* $y=50\text{km/hr}$ (speed of the second part)

Substituting these values:

$$\text{Average Speed}=\frac{2\times 80\times 50}{80+50}=\frac{8000}{130}=\frac{800}{13}\approx 61.538\text{km/hr}$$

Thus, the average speed for the entire $400\text{km}$ journey is approximately $61.53\text{km/hr}$.