Question

Из пункта А в пункт В по течению реки отправился плот. Одновременно с ним из пункта В в пункт А отправился катер, собственная скорость которого в 6 раз больше скорости течения реки. Встретив плот, катер повернул и поплыл обратно.Какую часть от пункта А до пункта В надо проплыть плоту, к тому моменту, когда катер вернется в пункт В.

Answer 1

Скорость плота равна скорости течения и равна х, тогда собственная скорость катера 6х, его же скорость по течению 7х, а против течения 5х. Пусть расстояние между А и В равно С, тогда до встречи плот проплыл х·Т, а катер 5х·Т.

Тогда

х·Т + 5х·Т = С

6х·Т = С

Катер вернулся, плывя по течению со скоростью 7х расстояние равное 5х·Т

Время, которое он затратил на обратный путь 5х·Т: 7х = 5/7 Т

За это время плот проплыл расстояние х·5/7 Т.

Всего он удалился от пункта А на х·Т + х·5/7 Т = 12/7 х·Т

Поскольку всё расстояние С = 6х·Т, то плот проплыл к моменту возвращения катера 12/7 х·Т : 6х·Т = 2/7

Ответ: плот проплыл 2/7 расстояния от А до В

 

Answer 2

Problem Analysis

We have a scenario where a raft starts from point A and travels downstream along a river. At the same time, a boat starts from point B and travels upstream towards point A. The boat's speed is 6 times greater than the speed of the river's current. The boat turns around when it meets the raft and returns to point B. We need to determine the fraction of the distance from point A to point B that the raft has traveled by the time the boat returns to point B.

Solution

Let's assume the speed of the river's current is v. Since the boat's speed is 6 times greater than the speed of the river's current, the boat's speed is 6v.

When the boat meets the raft, it has traveled a certain distance downstream from point B. At this point, the raft has traveled a certain distance upstream from point A. Let's call the distance traveled by the boat d1 and the distance traveled by the raft d2.

Since the boat's speed is 6 times greater than the speed of the river's current, the time taken by the boat to travel distance d1 is the same as the time taken by the raft to travel distance d2.

We can use the formula distance = speed × time to calculate the distances traveled by the boat and the raft.

For the boat: d1 = (6v) × t (Equation 1)

For the raft: d2 = v × t (Equation 2)

Since the time taken by the boat and the raft is the same, we can equate Equations 1 and 2:

(6v) × t = v × t

Simplifying the equation, we get:

6v × t = v × t

The time taken by the boat and the raft cancels out, leaving us with:

6v = v

Simplifying further, we find:

6 = 1

This is not a valid equation, which means there is no solution to this problem. The given scenario is not possible.

Conclusion

The given scenario is not possible because it leads to an invalid equation. Therefore, we cannot determine the fraction of the distance from point A to point B that the raft has traveled by the time the boat returns to point B.

Please let me know if there is anything else I can help you with.