3. Once Valera left home, walked to the cottage, painted 11 fence boards there, and returned home 2 hours after leaving. Another time, Valera and Olga went to the cottage together, painted 8 fence boards (without helping or hindering each other), and returned home together 3 hours after leaving. How many boards will Olga manage to paint alone if she needs to return home 1.5 hours after leaving? The physical abilities, diligence, and working conditions of Valera and Olga remain constant. (V. P. Fedorov)
Solution. This is a more complex version of problem 5 for 5th grade.

The strange result (that the characters accomplished less work in more time when working together) is explained by the different times spent walking, since the speed of "joint" walking is equal to the lower of the two walkers' speeds. The second time, Valera worked no more than $2 \cdot \frac{8}{11}$ hours, so they must have spent at least $3-\frac{16}{11}=\frac{17}{11}>1.5$ hours on the journey. This means that in one and a half hours, Olga would not have enough time to even walk to the cottage and back.

Answer: 0 boards.

Scoring. Only the answer - 0 points.

Evaluated progressions:

1) Understanding that two people walk at the speed of the slower one (this is stated explicitly or used in the solution) - 1 point.
2) With this in mind, it is indicated that Olga spends more than an hour on the journey (or at least an hour more than Valera, or something similar) - another +2 points.
3) It is calculated that in the second case, Valera would have completed the work alone in 16/11 hours (or that he would have completed it in less than 1.5 hours) - 2 points (added to progressions 1 and 2).

For example, the solution "In the second case, they spent an hour longer walking, so Olga spends an hour more on the journey than Valera, so in the third case, she will have a maximum of half an hour to work, and it's unclear what to do next" earns 3 points (progressions 1 and 2).

A solution like "In the second case, Valera would have worked alone for no more than $2 \cdot 8 / 11$ hours, and since it took them longer, Olga must have been in the way; so, alone, Olga would paint nothing (or a negative number of boards)" earns 2 points (only progression 3).