## 173. Math Puzzle 10/79

A tourist covered half the length of the planned hiking trail on the first day and a third of it on the second day. On the second day, the tourist had covered twelve kilometers less than on the first day.

How far did the tourist hike on the first and second day, and how much distance did he still need to cover on the third day?
The tourist covered one-sixth more of the distance on the second day than on the first day; for: $\frac{1}{2}-\frac{1}{3}=\frac{1}{6}$.

Since $6 \cdot 12=72$, the total length of the hiking trail was $72 \mathrm{~km}$. On the first day, 36 $\mathrm{km}$, on the second day, 24 $\mathrm{~km}$, and on the third day, 12 $\mathrm{~km}$ were covered.