Question

Из пункта А в пункт В по течению реки отправился плот.Одновременно навстречу ему из В вышла моторная лодка. Встретив плот, лодка сразу повернула и поплыла назад. Какую часть пути от А до В пройдёт плот к моменту возвращения лодки в пункт В, если собственная скорость лодки втрое больше скорости течения реки?

Answer 1

Х скорость течения реки, а также плота
3х собственная скорость лодки
S расстояние из А до В
До встречи плот по течению пройдет расстояние S1 за время S1/x, а лодка навстречу против течения пройдет расстояние (S-S1) со скоростью (3х-х=2х) за время (S-S1)/2x.  
S1/x=(S-S1)/2x
2S1=S-S1
S1=S/3
После встречи лодка проплыла по течению расстояние (S-S1=S-S/3=2S/3) со скоростью (3х+х=4х) за время 2S/3*4x=S/6x,  а тогда плот за это же время проплывет х*S/6x=S/6.  
Значит, плот к моменту возвращения лодки проплывет от А до В:
S/3+S/6=3S/6=S/2, т.е. половину пути
Ответ: половину пути от А до В.  

Answer 2

Problem Analysis

We are given that a raft starts from point A and travels downstream along a river. At the same time, a motorboat starts from point B and travels upstream towards the raft. When the boat meets the raft, it immediately turns around and heads back to point B. We need to determine what fraction of the distance from A to B the raft will have covered by the time the boat returns to point B. We are also given that the boat's speed is three times the speed of the river's current.

Solution

To solve this problem, we need to consider the relative speeds of the raft and the boat. Let's assume the speed of the river's current is v and the speed of the raft is r. Since the boat's speed is three times the speed of the river's current, the boat's speed is 3v.

When the boat meets the raft, the boat has traveled a certain distance upstream and the raft has traveled a certain distance downstream. Let's call the distance traveled by the boat x and the distance traveled by the raft y.

Since the boat's speed is three times the speed of the river's current, the boat's effective speed relative to the raft is 3v + v = 4v (the sum of the boat's speed and the river's current). Therefore, the boat takes x / (4v) time to meet the raft.

During this time, the raft has traveled a distance of y = r * (x / (4v)).

When the boat turns around and heads back to point B, it will take the same amount of time to return to point B as it took to meet the raft. Therefore, the boat will travel a distance of 2x in total.

To find the fraction of the distance from A to B covered by the raft when the boat returns to point B, we need to find the ratio of the distance traveled by the raft to the total distance from A to B.

Let's denote the total distance from A to B as d. The distance traveled by the raft is y = r * (x / (4v)) and the total distance traveled by the boat is 2x. Therefore, the fraction of the distance covered by the raft is:

Fraction = y / d = (r * (x / (4v))) / d

Now, let's substitute the given values into the equation and calculate the fraction.

Calculation

Given: - Boat's speed = 3 times the speed of the river's current - Boat's speed = 3v - Distance traveled by the boat = 2x - Distance traveled by the raft = r * (x / (4v)) - Total distance from A to B = d

To find the fraction of the distance covered by the raft, we need to calculate:

Fraction = (r * (x / (4v))) / d

Unfortunately, the specific values for the speed of the river's current, the distance traveled by the boat, and the total distance from A to B are not provided in the question. Therefore, we cannot calculate the exact fraction without these values.

However, we can use the given information to understand the relationship between the boat's speed, the raft's speed, and the fraction of the distance covered by the raft. We know that the boat's speed is three times the speed of the river's current, and the raft's speed is not specified. Therefore, we can conclude that the boat will cover a larger distance than the raft, and the fraction of the distance covered by the raft will be less than 1.

Conclusion

In conclusion, we cannot determine the exact fraction of the distance from A to B covered by the raft without the specific values for the speed of the river's current, the distance traveled by the boat, and the total distance from A to B. However, we can conclude that the fraction will be less than 1, as the boat's speed is three times the speed of the river's current, indicating that the boat will cover a larger distance than the raft.