Question

Теплоход проплывает расстояние между двумя городами по течению реки за 4ч, а по озеру - за 5ч. сколько времени потребуется плоту, чтобы преодолеть расстоян ие между этими двумя городами

Answer 1

4 часа потребуется плот, чтобы преодолеть расстояние между этими городами

Answer 2

Problem Analysis

We are given that a boat can travel a certain distance between two cities along a river in 4 hours and the same distance across a lake in 5 hours. We need to determine how long it would take a raft to cover the same distance between these two cities.

Solution

To solve this problem, we can use the concept of relative speed. The speed of the boat with the current of the river is different from its speed across the lake. Let's assume the speed of the boat in still water is b and the speed of the current is c.

When the boat is traveling along the river, its effective speed is the sum of the boat's speed and the speed of the current. Therefore, the boat's speed along the river is b + c.

When the boat is traveling across the lake, its effective speed is the difference between the boat's speed and the speed of the current. Therefore, the boat's speed across the lake is b - c.

We can set up the following equation to represent the distance traveled by the boat along the river and across the lake:

Distance along the river = (b + c) * 4

Distance across the lake = (b - c) * 5

Since the distance traveled along the river and across the lake is the same, we can equate the two equations:

(b + c) * 4 = (b - c) * 5

Simplifying this equation will allow us to solve for the speed of the current (c):

4b + 4c = 5b - 5c

9c = b

Now that we have the relationship between the speed of the current and the speed of the boat, we can determine the time it would take for a raft to cover the same distance between the two cities. Since a raft has no engine and is solely dependent on the current, its speed will be equal to the speed of the current (c).

Therefore, the time it would take for the raft to cover the distance between the two cities is 9c.

Answer

The raft would take 9c hours to cover the distance between the two cities, where c is the speed of the current.

Please note that the specific values for the speed of the boat and the current were not provided in the question, so we cannot determine the exact time it would take for the raft to cover the distance.