Question

Моторная лодка проплыла расстояние между двумя пристанями по течению реки за 6 ч. Это же расстояние против течения реки лодка проплыла за 8 ч. Найдите скорость лодки, если течение реки 2,5 км/ ч

Answer 1

Скорость лодки наверное 43 км

Answer 2

Problem Analysis

We are given that a motorboat traveled a certain distance between two docks in 6 hours with the current of a river, and the same distance against the current in 8 hours. We are also given that the current of the river is 2.5 km/h. We need to find the speed of the boat.

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 + 2.5) km/h.

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 - 2.5) km/h.

We can use the formula distance = speed × time to find the distance traveled by the boat in both cases.

According to the problem, the boat traveled the same distance in both cases. Let's call this distance d km.

Using the formula, we can write the following equations:

1. When traveling with the current: d = (x + 2.5) × 6. 2. When traveling against the current: d = (x - 2.5) × 8.

We can solve these equations to find the value of x, which represents the speed of the boat in still water.

Let's solve the equations:

d = (x + 2.5) × 6 --> Equation 1

d = (x - 2.5) × 8 --> Equation 2

By equating the right sides of the equations, we have:

(x + 2.5) × 6 = (x - 2.5) × 8

Simplifying the equation:

6x + 15 = 8x - 20

20 + 15 = 8x - 6x

35 = 2x

x = 35/2

x = 17.5

Therefore, the speed of the boat in still water is 17.5 km/h.

Answer

The speed of the boat is 17.5 km/h.