Question

Пожалуйста помогите! Условие и решение! Расстояния между двумя пристанями по течению реки катер проходит за 8 ч, а плот - за 72 ч. Сколько времени потратит катер на тот же путь по озеру?

Answer 1

Ответ:

9 часов.

Пошаговое объяснение:

Расстояние между пристанями примем за единицу.

1) 1 : 8 = 1/8 - скорость катера по течению реки;

2) 1 : 72 = 1/72 - скорость плота = скорости течения реки;

3) 1/8 - 1/72 = 9/72 - 1/72 = 8/72 = 1/9 - собственная скорость катера;

4) 1 : 1/9 = 1 * 9/1 = 9 (ч) - время, которое потратит катер на тот же путь по озеру.

Ответ: 9 часов.

Answer 2

Problem Analysis

We are given that a boat travels between two docks along a river in 8 hours, while a raft takes 72 hours to cover the same distance. We need to determine how long it will take the boat to cover the same distance on a lake.

Solution

To solve this problem, we can use the concept of relative speed. The relative speed of the boat with respect to the raft is the difference in their speeds. Let's denote the speed of the boat as B and the speed of the raft as R.

We are given that the boat takes 8 hours to cover the distance on the river, so we can calculate the speed of the boat using the formula:

Speed = Distance / Time

Let's denote the distance between the docks as D. Therefore, the speed of the boat on the river is:

B = D / 8

Similarly, we can calculate the speed of the raft using the formula:

R = D / 72

Now, we need to find the time it takes for the boat to cover the same distance on the lake. Let's denote this time as T. Since the boat is now traveling on a lake, there is no current to consider. Therefore, the speed of the boat on the lake will be the same as its speed on the river, which is B.

Using the formula Speed = Distance / Time, we can write:

B = D / T

Now, we can substitute the value of B from the equation we derived earlier:

D / 8 = D / T

To find T, we can cross-multiply and solve for T:

D * T = D * 8

T = 8

Therefore, the boat will take 8 hours to cover the same distance on the lake.

Conclusion

The boat will take 8 hours to cover the same distance on the lake as it takes to cover the distance between the two docks along the river.