Task 1. Little Red Riding Hood decided to visit her grandmother, whose cottage was 1 km away from her house. The wolf did not encounter her that day, so she walked the same route to and from. On flat sections, her speed was 4 km/h, uphill - 3 km/h, and downhill - 6 km/h. How long was she on the way?
Answer: Half an hour.

Solution. Consider any inclined section of the path of length $s$. Climbing it, Red Riding Hood will spend $s / 3$ time, descending $-s / 6$, in total -- $s\left(\frac{1}{3}+\frac{1}{6}\right)=\frac{s}{2}$. Therefore, her average speed on this section is $2 s: \frac{s}{2}=4$. Thus, the average speed on all sections is the same and equals 4 km/h. The entire path of the girl is 2 km, so she will spend half an hour on the journey.

Criteria. 0 points for an answer without justification, 1 point for a solution on separate examples. 7 points for a complete justification.