Question

3. Никулин, Вицин, Моргунов и Гайдай опаздывают на съёмки. Ночь. Кругом — темень. Фонарик один на всех. Съёмки эти проходят на противоположном берегу речки. Мостик слабенький, может выдержать максимум двух человек одновременно. У режиссёра и актёров есть 17 минут для того, чтобы перебраться на другой берег. Идти без фонарика нельзя. Скорости пересечения моста такие: Никулин тратит на переход 1 минуту, Вицин — 2, Гайдай — 5, Моргунов — 10. Когда мостик переходят два человека, скорость обоих равна скорости самого медленного из пары.

Answer 1

Сначала переходят Никулин и Вицин  - 2 минуты.
Вицин возвращается назад - 2 минуты.
Переходят Гайдай и Моргунов - 10 минут.
Никулин назад - 1 минута.
Переходят Никулин и Вицин - 2 минуты.
Всего 2+2+10+1+2 = 17 минут и все на другом берегу.

Answer 2

Problem Analysis

The problem describes a scenario where four individuals (Nikulin, Vitsin, Morgunov, and Gaidai) are late for a shoot. They need to cross a weak bridge to get to the opposite bank of a river where the shoot is taking place. The bridge can only support a maximum of two people at a time. Each person has a different crossing speed, and they have a total of 17 minutes to complete the crossing. The goal is to determine the minimum time required for all four individuals to reach the other side.

Solution

To solve this problem, we need to find the optimal combination of people crossing the bridge to minimize the total time. We can start by considering the two slowest individuals, as they will determine the overall crossing time.

Let's analyze the possible combinations:

1. Nikulin and Vitsin cross the bridge together: - Time taken: 2 minutes (Vitsin) + 1 minute (Nikulin) = 3 minutes - Remaining time: 17 minutes - 3 minutes = 14 minutes - Morgunov crosses the bridge with the flashlight: 10 minutes - Remaining time: 14 minutes - 10 minutes = 4 minutes - Gaidai crosses the bridge with the flashlight: 5 minutes - Total time: 3 minutes (Nikulin and Vitsin) + 10 minutes (Morgunov) + 5 minutes (Gaidai) = 18 minutes

2. Nikulin and Morgunov cross the bridge together: - Time taken: 10 minutes (Morgunov) + 1 minute (Nikulin) = 11 minutes - Remaining time: 17 minutes - 11 minutes = 6 minutes - Vitsin crosses the bridge with the flashlight: 2 minutes - Remaining time: 6 minutes - 2 minutes = 4 minutes - Gaidai crosses the bridge with the flashlight: 5 minutes - Total time: 11 minutes (Nikulin and Morgunov) + 2 minutes (Vitsin) + 5 minutes (Gaidai) = 18 minutes

3. Nikulin and Gaidai cross the bridge together: - Time taken: 5 minutes (Gaidai) + 1 minute (Nikulin) = 6 minutes - Remaining time: 17 minutes - 6 minutes = 11 minutes - Morgunov crosses the bridge with the flashlight: 10 minutes - Remaining time: 11 minutes - 10 minutes = 1 minute - Vitsin crosses the bridge with the flashlight: 2 minutes - Total time: 6 minutes (Nikulin and Gaidai) + 10 minutes (Morgunov) + 2 minutes (Vitsin) = 18 minutes

Based on the analysis, it can be concluded that regardless of the combination chosen, the total time required for all four individuals to reach the other side is 18 minutes.

Note: The problem does not specify any constraints or rules for optimizing the crossing time. Therefore, the solution provided above is based on the assumption that the goal is to minimize the total time required for all four individuals to reach the other side.

Conclusion

In the given scenario, regardless of the combination chosen, the total time required for all four individuals (Nikulin, Vitsin, Morgunov, and Gaidai) to reach the other side is 18 minutes.