Question

Из пункта А вниз по течению реки одновременно отплыли плот и катер. А навстречу им в тот же момент из пункта Б отправился второй такой же катер. Когда первый катер достигнет пункта Б? К чему будет ближе плот, к пункту А или ко второму катеру?

Answer 1

Problem Analysis

We have a scenario where a raft and a boat start simultaneously from point A and travel downstream on a river. At the same time, another boat starts from point B and travels upstream. We need to determine when the first boat will reach point B and whether the raft will be closer to point A or the second boat.

Solution

To solve this problem, we need to consider the relative speeds of the boats and the raft. Let's assume that the speed of the raft is R, the speed of the first boat is B1, and the speed of the second boat is B2. We also need to know the distance between points A and B, which we'll call D.

Since the first boat and the raft are traveling downstream, their effective speeds will be the sum of their speeds and the speed of the river. Similarly, the second boat is traveling upstream, so its effective speed will be the difference between its speed and the speed of the river.

Let's denote the speed of the river as V. Therefore, the effective speed of the raft will be R + V, the effective speed of the first boat will be B1 + V, and the effective speed of the second boat will be B2 - V.

To determine when the first boat will reach point B, we can use the formula:

Time = Distance / Speed

The distance between points A and B is D, and the effective speed of the first boat is B1 + V. Therefore, the time taken by the first boat to reach point B is:

Time1 = D / (B1 + V)

Now, let's analyze the position of the raft relative to point A and the second boat. Since the raft and the second boat started at the same time, their travel times will be the same. Therefore, the distance traveled by the raft will be the effective speed of the raft multiplied by the time taken by the first boat to reach point B:

Distance traveled by the raft = (R + V) * Time1

If the distance traveled by the raft is less than D, it