5) A cyclist climbs a hill at a constant speed $v$ and then descends the same road at a constant speed that is three times the previous speed. The average speed for the entire round trip is. .
(A) $\frac{3}{4} v$
(B) $\frac{4}{3} v$
(C) $\frac{3}{2} v$
(D) $2 v$
(E) depends on the length of the road
5) The answer is $\mathbf{( C )}$. Let $s$ be the length of the journey (one way), the travel times for the outbound and return trips are $t_{1}=\frac{s}{v}$ (outbound), $t_{2}=\frac{s}{3 v}$ (return). The average speed for the entire trip will therefore be:

$$
\frac{2 s}{t_{1}+t_{2}}=\frac{2 s}{\frac{s}{v}+\frac{s}{3 v}}=2 s \frac{3 v}{4 s}=\frac{3}{2} v
$$