2. Darijan and Vedran rode their motorcycles from Skopje to Ohrid. Darijan drove the first third of the distance at a speed of 20 kilometers per hour, the second third at a speed of 30 kilometers per hour, and the last third at a speed of 40 kilometers per hour. Vedran drove the first third of the time at a speed of 20 kilometers per hour, the second third of the time at a speed of 30 kilometers per hour, and the last third of the time at 40 kilometers per hour. Which of the two arrived in Ohrid faster?
Solution. We calculate the average speeds of the two. Denoting by $v_{1}, v_{2}, v_{3}$ the speeds of 20 kilometers per hour, 30 kilometers per hour, and 40 kilometers per hour, respectively, for Darijan we have:

$$
\frac{3 s}{v_{s r}}=\frac{s}{v_{1}}+\frac{s}{v_{2}}+\frac{s}{v_{3}}
$$

where $s$ is the length of one-third of the route from Skopje to Ohrid. Thus,

$$
v_{S r}(D)=\frac{3}{\frac{1}{v_{1}}+\frac{1}{v_{2}}+\frac{1}{v_{3}}}=27.7 \mathrm{~km} / \mathrm{h}
$$

On the other hand, for Vedran we have: $3 t v_{s r}=v_{1} t+v_{2} t+v_{3} t$, where $t$ is one-third of the duration of his journey. Therefore,

$$
v_{s r}(V)=\frac{v_{1}+v_{2}+v_{3}}{3}=30 \mathrm{~km} / \mathrm{h}
$$

We conclude that Vedran arrived in Ohrid faster.