Given that, the distances travelled by the body
are in ratio $1: 2$.
Let us suppose that $s$ is the distance, the body travels with speed $v_1$. Then, $2 s$ will be the distance
travelled by the body with speed $v_2$. This scenario is shown in the line-diagram below


For $A$ to $C$,
$\begin{aligned}
& \text { Average speed }=\frac{\text { Total distance travelled }}{\text { Total time taken }} \\
& \qquad \begin{aligned}
v_{\text {avg }} & =\frac{s_1+s_2}{t_1+t_2}=\frac{s+2 s}{\frac{s}{v_1}+\frac{2 s}{v_2}} \\
& =\frac{3 s}{s\left[\frac{1}{v_1}+\frac{2}{v_2}\right]}=\frac{3}{\left[\frac{v_2+2 v_1}{v_1 v_2}\right]}=\frac{3 v_1 v_2}{v_2+2 v_1}
\end{aligned}
\end{aligned}$