5. The conditions of the road between Town $A$ and Town $B$ can be classified as up slope, horizontal or down slope and total length of each type of road is the same. A cyclist travels from Town $A$ to Town $B$ with uniform speeds $8 \mathrm{~km} / \mathrm{h}, 12 \mathrm{~km} / \mathrm{h}$ and $24 \mathrm{~km} / \mathrm{h}$ on the up slope, horizontal and down slope road respectively. What is the average speed of his journey?
(A) $12 \mathrm{~km} / \mathrm{h}$;
(B) $\frac{44}{3} \mathrm{~km} / \mathrm{h}$;
(C) $16 \mathrm{~km} / \mathrm{h}$;
(D) $17 \mathrm{~km} / \mathrm{h}$;
(E) $18 \mathrm{~km} / \mathrm{h}$.
5. Ans: (A)
Let the distance between Town $A$ and Town $B$ be $3 s$. The total time taken for up slope, horizontal and down slope road are $\frac{\pi}{8}, \frac{s}{12}$ and $\frac{s}{24}$ respectively. His average speed for the whole journey is $\frac{3 s}{\frac{s}{8}+\frac{s}{12}+\frac{s}{24}}=12 \mathrm{~km} / \mathrm{h}$.