Question

№5 Вдоль 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 52 го фонаря, Борис был у 318-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:

370

Пошаговое объяснение:

318 + 52 как то так/). мир

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. Alla starts from the first lamp (lamp 1), while Boris starts from the 400th lamp. We are also given that when Alla reaches the 52nd lamp, Boris is at the 318th lamp. We need to determine at which lamp they will meet.

Solution

To solve this problem, we can use the concept of relative speed. The relative speed between Alla and Boris is the sum of their individual speeds. Let's assume that Alla's speed is A and Boris's speed is B.

We know that when Alla reaches the 52nd lamp, Boris is at the 318th lamp. This means that Alla has covered a distance of 51 lamps, while Boris has covered a distance of (400 - 318) = 82 lamps. Since they are walking towards each other, the sum of the distances covered by Alla and Boris should be equal to the total distance between the 52nd and 318th lamps.

Let's set up an equation to represent this:

Distance covered by Alla + Distance covered by Boris = Total distance between the 52nd and 318th lamps

51 * A + 82 * B = (318 - 52) * D

where D is the distance between two consecutive lamps.

Since the distance between two consecutive lamps is the same, we can cancel it out from both sides of the equation:

51 * A + 82 * B = 266 * D

Now, we need to find the values of A and B that satisfy this equation. We can use trial and error to find the values that work.

Let's start with A = 1 and B = 1:

51 * 1 + 82 * 1 = 133

Since 133 is not equal to 266, we need to try different values of A and B.

Let's try A = 2 and B = 1:

51 * 2 + 82 * 1 = 184

Still not equal to 266. Let's try A = 3 and B = 1:

51 * 3 + 82 * 1 = 235

Still not equal to 266. Let's try A = 4 and B = 1:

51 * 4 + 82 * 1 = 286

Now we have a match! A = 4 and B = 1 satisfy the equation.

This means that Alla's speed is 4 times the speed of Boris. Therefore, if Alla takes 1 step, Boris takes 4 steps.

Since Alla starts from the first lamp (lamp 1) and Boris starts from the 400th lamp, their meeting point will be closer to Alla's starting point. In fact, it will be at a distance of 51 steps from Alla's starting point.

Therefore, their meeting point will be at the 53rd lamp.

Answer

The meeting point of Alla and Boris will be at the 53rd lamp.