Question

Лодка по течению реки за 7 часов прошла такое же расстояние, как за 9 часов против течения. Найти скорость течения, если собственная скорость лодки равна 18 км/ч. помогите пожалуйста.

Answer 1

Х (км/ч)-скорсть течения реки
18+х (км/ч)-скорость по течению
18-х (км/ч)-скорость против течения
По течению 7час, против течения 9час.

7(18+х)=9(18-х)
126+7х=162-9х
7х+9х=162-126
16х=36
х=36:16
х=2,25 (км/ч)-скорость течения реки

Answer 2

Problem Analysis

We are given that a boat traveled the same distance in 7 hours downstream as it did in 9 hours upstream. We need to find the speed of the current, given that the boat's speed in still water is 18 km/h.

Solution

Let's assume the speed of the current is x km/h.

When the boat is traveling downstream, its effective speed is the sum of its own speed and the speed of the current. So, the effective speed is 18 + x km/h.

When the boat is traveling upstream, its effective speed is the difference between its own speed and the speed of the current. So, the effective speed is 18 - x km/h.

We are given that the boat traveled the same distance in both cases. Let's denote the distance as d km.

According to the given information, the time taken to travel downstream is 7 hours, and the time taken to travel upstream is 9 hours.

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

For downstream: 18 + x = d / 7 For upstream: 18 - x = d / 9 We can solve these two equations to find the value of x, which represents the speed of the current.

Let's solve the equations:

From equation d = (18 + x) * 7 From equation d = (18 - x) * 9 Since both equations and represent the same distance d, we can equate them:

(18 + x) * 7 = (18 - x) * 9

Let's solve this equation to find the value of x.

Calculation

Expanding the equation:

126 + 7x = 162 - 9x

Combining like terms:

16x = 36

Dividing both sides by 16:

x = 36 / 16 = 2.25

Answer

The speed of the current is 2.25 km/h.

Explanation

The boat's speed in still water is 18 km/h. When it travels downstream, the speed of the current adds to its own speed, making it faster. When it travels upstream, the speed of the current subtracts from its own speed, making it slower. By setting up equations based on the given information and solving them, we find that the speed of the current is 2.25 km/h.