Knight Milivoj was preparing to go to Veselín for a tournament. The tournament takes place on Wednesday. Since the journey from Knight's home, Rytířov, to Veselín would take two days, he set off on Monday. The road leads through two other towns, Kostín and Zubín. On the first day of travel, he covered 25 miles and spent the night in Zubín. On the second day, Tuesday, he happily arrived in Veselín. He won the tournament convincingly, so when he returned on Thursday, he traveled faster. He traveled 6 miles more than on Monday, so he spent the night in Kostín. On Friday, he traveled the remaining 11 miles to Rytířov. Determine the distance between Zubín and Veselín. 

(M. Petrová)
Let's first visualize the situation from the assignment.

The journey to the tournament:

![](https://cdn.mathpix.com/cropped/2024_04_17_2fa1f9d116e69791db0fg-3.jpg?height=237&width=942&top_left_y=2006&top_left_x=563)

The journey from the tournament:

![](https://cdn.mathpix.com/cropped/2024_04_17_2fa1f9d116e69791db0fg-3.jpg?height=245&width=942&top_left_y=2379&top_left_x=563)

Since on Thursday Milivoj rode 6 miles more than on Monday, he must have ridden from Veselín to Kostín $25+6=31$ (miles) on Thursday.

This means that the total distance from Rytířov to Veselín measures $11+31=42$ (miles). Since the distance between Rytířov and Zubín is 25 miles, the distance between Zubín and Veselín must be $42-25=17$ (miles).

Evaluation. 2 points for determining the distance between Kostín and Veselín; 2 points for determining the distance between Rytířov and Veselín; 2 points for determining the distance between Zubín and Veselín. Always award one point for the numerical value and the second point for the appropriate explanation. (If the solution lacks any explanation of the procedure, award no more than 3 points for this task.)

Note. Instead of the calculations in the second paragraph, the distances can be considered as follows: Since the distance between Rytířov and Zubín is 25 miles and between Rytířov and Kostín is 11 miles, the distance between Kostín and Zubín is $25-11=14$ (miles). So the distance between Zubín and Veselín must be $31-14=17$ (miles). The evaluation in this case is similar.

Alternative solution. On Monday, Milivoj rode two segments of the entire journey: the first from Rytířov to Kostín, the second from Kostín to Zubín. On Thursday, he rode two segments as well: from Kostín to Zubín and from Zubín to Veselín. (The fact that Knight Milivoj traveled in the opposite direction does not affect this reasoning.) This means that he traveled the segment from Kostín to Zubín on both days. If he rode 6 miles more on Thursday, the segment from Zubín to Veselín must be 6 miles longer than the segment from Rytířov to Kostín. Since the distance from Rytířov to Kostín is 11 miles, the distance between Zubín and Veselín must be $11+6=17$ (miles).

Evaluation. Award 5 points (or fewer based on the quality of the explanation) for comparing the Monday and Thursday journeys and explaining why the segment between Zubín and Veselín is 6 miles longer than the segment between Rytířov and Kostín. Award the last 1 point for the final result of 17 miles.