Question

Пароход, собственная скорость которого равна 24 км/ч, прошёл за 1,4 часа по течению реки такое же расстояние, как и за 1,8 часа против течения. Чему равна скорость течения реки?

Answer 1

Пусть скорость течения реки х
Тогда скорость парохода по течению 24+х км/ч
Против течения 24-х км/ч
По течению прошёл (24+х)*1,4 км
Против течения (24-х)*1,8 км
Расстояние одинаковое, значит
1,4*(24+х)=1,8*(24-х)
33,6+1,4х=43,2-1,8х
1,4х+1,8х=43,2-33,6
3,2х=9,6
Х=9,6:3,2
Х=3
Ответ: 3 км/ч

Answer 2

Problem Analysis

We are given that a steamboat with a speed of 24 km/h traveled the same distance in 1.4 hours downstream as it did in 1.8 hours upstream. We need to determine the speed of the river's current.

Solution

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

When the steamboat is traveling downstream, its effective speed is the sum of its own speed and the speed of the current. Therefore, the effective speed downstream is 24 + x km/h.

When the steamboat is traveling upstream, its effective speed is the difference between its own speed and the speed of the current. Therefore, the effective speed upstream is 24 - x km/h.

We are given that the steamboat traveled the same distance downstream in 1.4 hours as it did upstream in 1.8 hours. This means that the distance traveled downstream is equal to the distance traveled upstream.

Let's denote the distance traveled downstream as D.

According to the formula distance = speed × time, we can write the following equations:

Downstream: Distance = (24 + x) × 1.4

Upstream: Distance = (24 - x) × 1.8

Since the distances are equal, we can set up the following equation:

(24 + x) × 1.4 = (24 - x) × 1.8

Now we can solve this equation to find the value of x.

Calculation

Let's solve the equation:

(24 + x) × 1.4 = (24 - x) × 1.8

Expanding the equation:

33.6 + 1.4x = 43.2 - 1.8x

Rearranging the equation:

3.2x = 9.6

Dividing both sides by 3.2:

x = 3

Answer

The speed of the river's current is 3 km/h.

Explanation

The steamboat traveled the same distance downstream in 1.4 hours as it did upstream in 1.8 hours. By setting up and solving an equation based on the distances and speeds, we found that the speed of the river's current is 3 km/h.