A vehicle covers half the distance with uniform speed $v_1$ and the other half with uniform speed $v_2$. The average speed of the vehicle is

Let the total distance covered by the vehicle be $2d$.
The distance for each half is $d$.
The time taken to cover the first half is:

$$t_1=\frac{d}{v_1}$$

The time taken to cover the second half is:

$$t_2=\frac{d}{v_2}$$

The total time $T$ is given by:

$$T=t_1+t_2=\frac{d}{v_1}+\frac{d}{v_2}=d\left(\frac{v_1+v_2}{v_1{v}_2}\right)$$

Average speed ($v_{\text{avg}}$) is defined as the total distance divided by the total time:

$$v_{\text{avg}}=\frac{2d}{T}=\frac{2d}{d\left(\frac{v_1+v_2}{v_1{v}_2}\right)}=\frac{2v_1{v}_2}{v_1+v_2}$$