Question

доль прямой аллеи через равные промежутки стоят 400 фонарей, пронумерованные по порядку числами от 1 до 400. Одновременно с разных концов аллеи навстречу друг другу с разными постоянными скоростями вышли Алла и Борис (Алла — от первого фонаря, Борис — от четырехсотого). Когда Алла была у 55‑го фонаря, Борис был у 321‑го фонаря. У какого фонаря произойдет их встреча? Если встреча произойдет между двумя фонарями, то в ответе укажите меньший номер из этих двух.

Answer 1

Ответ:

266

Пошаговое объяснение:

                                                 

Answer 2

Problem Analysis

We are given that there are 400 lamps numbered from 1 to 400, placed at equal intervals along a straight alley. Two people, Alla and Boris, start walking towards each other from opposite ends of the alley. They have different constant speeds. We are asked to determine at which lamp they will meet.

Solution

Let's analyze the problem step by step:

1. Alla starts from the first lamp (lamp 1), and Boris starts from the last lamp (lamp 400). 2. When Alla reaches the 55th lamp, Boris is at the 321st lamp. 3. We need to find the lamp where they will meet.

To solve this problem, we can use the concept of relative speed. The relative speed is the difference between the speeds of two objects moving in opposite directions.

Let's assume that Alla's speed is A and Boris's speed is B. The relative speed between them is A + B.

Now, let's calculate the relative speed between Alla and Boris:

- When Alla reaches the 55th lamp, she has covered a distance of 55 lamps. - At the same time, Boris has covered a distance of (400 - 321) = 79 lamps. - The relative speed between them is (55 + 79) = 134 lamps.

Since they are moving towards each other, the total distance between them is 400 lamps. Therefore, the time taken to meet each other is:

Time = Distance / Relative Speed Time = 400 / 134

Now, let's calculate the time taken to meet:

Time = 2.985 seconds (approximately)

To find the lamp where they will meet, we can multiply the time taken by Alla's speed and add it to the position of Alla when she started (lamp 55):

Lamp number = Alla's starting position + (Alla's speed * Time) Lamp number = 55 + (A * 2.985)

Unfortunately, we don't have the exact values for Alla's speed or the time taken. Therefore, we cannot determine the exact lamp number where they will meet.

However, if the meeting occurs between two lamps, we can provide the smaller lamp number as the answer.

Note: The exact lamp number where Alla and Boris will meet cannot be determined without knowing their speeds or the exact time taken.

Conclusion

Based on the given information, we can determine the relative speed between Alla and Boris and calculate the time taken to meet. However, without knowing the exact speeds or the time taken, we cannot determine the exact lamp number where they will meet. If the meeting occurs between two lamps, we can provide the smaller lamp number as the answer.