Task 1 - 270721 Jörg undertook a three-day cycling tour during his vacation. He covered half of the total planned route on the first day and one-third of the total length on the second day.

On the second day, Jörg cycled 24 km less than on the first day.

Determine the length of the route that Jörg still had left for the third day!
From $\frac{1}{2}-\frac{1}{3}=\frac{1}{6}$ it follows that Jörg covered $\frac{1}{6}$ of the total planned distance for all three days more on the first day than on the second day. Since $6 \cdot 24=144$, the total hiking distance was $144 \mathrm{~km}$.

On the first day, Jörg thus covered $144 \mathrm{~km} : 2 = 72 \mathrm{~km}$, and on the second day $144 \mathrm{~km} : 3 = 48 \mathrm{~km}$. Therefore, for the third day, Jörg had $144 - 72 - 48 = 24$ km left, which is $24 \mathrm{~km}$.