Question

По дороге в школу третьеклассник Коля преодолел 27 луж.Догога заняла 15 мин. Докажите что найдется две лужи с паузой менее 35 сек.

Answer 1

Problem Analysis

To prove that there are two puddles with a pause of less than 35 seconds, we need to analyze the given information.

We know that on the way to school, Kolya, a third-grader, crossed 27 puddles, and the journey took 15 minutes. However, we don't have any specific information about the duration of each puddle or the pause between them.

To prove that there are two puddles with a pause of less than 35 seconds, we need to consider the worst-case scenario. In this scenario, Kolya crosses all 27 puddles without any pause, and the entire journey time is spent crossing the puddles.

Proof

Let's assume that Kolya crosses each puddle in the minimum possible time, which is 15 seconds, and there is no pause between the puddles.

If Kolya crosses 27 puddles in 15 minutes, the average time taken to cross each puddle is:

Average time per puddle = Total time / Number of puddles = 15 minutes / 27 puddles

Converting the time to seconds:

Average time per puddle = (15 minutes * 60 seconds) / 27 puddles

Simplifying:

Average time per puddle ≈ 33.33 seconds

Since the average time per puddle is approximately 33.33 seconds, it is possible that there are two puddles with a pause of less than 35 seconds.

However, it's important to note that this proof assumes the worst-case scenario, where there is no pause between the puddles. In reality, there could be pauses between some of the puddles, which would increase the likelihood of finding two puddles with a pause of less than 35 seconds.

Therefore, based on the given information, it is possible to find two puddles with a pause of less than 35 seconds.

Conclusion

Based on the analysis and proof above, it is possible to find two puddles with a pause of less than 35 seconds on Kolya's way to school. However, it's important to consider that this proof assumes the worst-case scenario, where there is no pause between the puddles. In reality, there could be pauses between some of the puddles, which would increase the likelihood of finding two puddles with a pause of less than 35 seconds.