I4.4 A boy walks from home to school at a speed of $p \mathrm{~km} / \mathrm{h}$ and returns home along the same route at a speed of $3 \mathrm{~km} / \mathrm{h}$. If the average speed for the double journey is $\frac{24}{q} \mathrm{~km} / \mathrm{h}$, find $q$.
Let the distance of the single journey be $x \mathrm{~km}$.
$$
\begin{aligned}
\frac{24}{q} & =\frac{2 x}{\frac{x}{4}+\frac{x}{3}} \\
\frac{24}{q} & =\frac{24}{7} \\
\Rightarrow q & =7
\end{aligned}
$$