68. When Vasya Verkhoglyadkin was given this problem: "Two tourists set out from $A$ to $B$ simultaneously. The first tourist walked half of the total time at a speed of $5 \mathrm{km} /$ h, and the remaining half of the time at a speed of 4 km/h. The second tourist walked the first half of the distance at a speed of 5 km/h, and the second half at a speed of 4 km/h. Who will arrive in $B$ first?" - he declared: "It's clear that they will arrive in $B$ simultaneously." What do you think?
68. If the length of the path is $a$ km and the first tourist walked it in $x$ hours, then $5 \cdot \frac{x}{2} + 4 \cdot \frac{x}{2} = a$, from which $x = \frac{2a}{9}$. The second tourist walked this path in $\frac{a}{2 \cdot 5} + \frac{a}{2 \cdot 4} = \frac{9a}{40}$. Let's compare $\frac{2a}{9}$ and $\frac{9a}{40}, \frac{2a}{9} = \frac{18a}{81}; \frac{9a}{40} = \frac{18a}{80}$. Since $\frac{18a}{81} < \frac{18a}{80}$, the first tourist spent less time on the entire path than the second, which means he will arrive in $B$ earlier than the second.