Question

Лодка проходит за 1/5 ​ часа по течению реки такое же расстояние, какое проходит за 1/4 ​ часа против течения. Найдите собственную скорость лодки, если скорость течения реки равна 4 км/ч.

Answer 1

Ответ:

36 км/ч.

Объяснение:

Пусть собственная скорость лодки х км/ч, тогда её скорость по течению х+4 км/ч, против течения х-4 км/ч. Составим уравнение:

1/5(х+4) = 1/4(х-4)

0,2х+0,8=0,25х-1

0,05х=1,8

х=36

Собственная скорость лодки 36 км/ч.

Answer 2

Problem Analysis

We are given that a boat takes 1/5 of an hour to travel a certain distance with the current of a river, and it takes 1/4 of an hour to travel the same distance against the current. We need to find the speed of the boat in still water, given that the speed of the river current is 4 km/h.

Solution

Let's assume the speed of the boat in still water is x km/h.

When the boat is traveling with the current, its effective speed is the sum of its speed in still water and the speed of the current. So, the effective speed is x + 4 km/h.

Similarly, when the boat is traveling against the current, its effective speed is the difference between its speed in still water and the speed of the current. So, the effective speed is x - 4 km/h.

We are given that the boat takes 1/5 of an hour (or 1/5 * 60 = 12 minutes) to travel a certain distance with the current, and it takes 1/4 of an hour (or 1/4 * 60 = 15 minutes) to travel the same distance against the current.

Using the formula speed = distance / time, we can set up the following equations:

1. When traveling with the current: - Distance = Speed * Time - Distance = (x + 4) * 12/60 (converting 12 minutes to hours) - Distance = (x + 4) * 1/5

2. When traveling against the current: - Distance = Speed * Time - Distance = (x - 4) * 15/60 (converting 15 minutes to hours) - Distance = (x - 4) * 1/4

Since the distances traveled in both cases are the same, we can equate the two equations:

(x + 4) * 1/5 = (x - 4) * 1/4

Simplifying the equation:

4(x + 4) = 5(x - 4)

4x + 16 = 5x - 20

16 + 20 = 5x - 4x

36 = x

Therefore, the speed of the boat in still water is 36 km/h.

Answer

The speed of the boat in still water is 36 km/h.