5. 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 9 fence boards (without helping or hindering each other), and returned home together 3 hours after leaving. How many boards will Olga be able to paint alone if she needs to return home 1 hour after leaving? The physical abilities, diligence, and working conditions of Valera and Olga remain unchanged.

(V. P. Fedorov)
Solution. The strange result (working together for a longer time, the characters managed to do less work) 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, Valery's working time decreased, which means the travel time increased by more than an hour; hence, Olga spends more than an hour on the trip to the cottage and back. Therefore, in an hour, she wouldn't even have time to get there and return.

Answer: 0 boards

Criteria. Only the answer - 0 points. Understanding that two people walk at the speed of the slower walker (i.e., Olga) - 2 points.