Question

Теплоход прошел по течению реки 96 км и столько же против течения,затратив на весь путь 10 часов.Скорость теплохода в стоячей воде равна 20 км/ч. Определите скорость течения воды.

Answer 1

96*2=192км прошел всего
10*20=200км прошел бы по стоячей воде
(200-192)/2=4км/ч скорость течения
Проверка
96/(20+4)+96/(20-4)=10
Ответ: 4км/ч

Answer 2

См фото,
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Answer 3

Problem Analysis

We are given that a boat traveled 96 km downstream and the same distance upstream, taking a total of 10 hours for the entire journey. The speed of the boat in still water is given as 20 km/h. We need to determine the speed of the river current.

Solution

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

When the boat is traveling downstream, its effective speed is the sum of its speed in still water and the speed of the current. Therefore, the boat's speed downstream is (20 + x) km/h.

When the boat is traveling upstream, its effective speed is the difference between its speed in still water and the speed of the current. Therefore, the boat's speed upstream is (20 - x) km/h.

We are given that the boat traveled 96 km both downstream and upstream, taking a total of 10 hours for the entire journey. We can set up the following equation to represent this:

96 / (20 + x) + 96 / (20 - x) = 10

To solve this equation, we can multiply both sides by the least common multiple (LCM) of the denominators, which is (20 + x)(20 - x). This will eliminate the denominators and allow us to solve for x.

Let's solve the equation step by step:

1. Multiply both sides of the equation by (20 + x)(20 - x): 96(20 - x) + 96(20 + x) = 10(20 + x)(20 - x)

2. Simplify both sides of the equation: 1920 - 96x + 1920 + 96x = 200(400 - x^2)

3. Combine like terms: 3840 = 200(400 - x^2)

4. Divide both sides of the equation by 200: 19 = 400 - x^2

5. Rearrange the equation: x^2 = 400 - 19

6. Simplify: x^2 = 381

7. Take the square root of both sides: x = √381

Using a calculator, we find that √381 ≈ 19.52.

Therefore, the speed of the river current is approximately 19.52 km/h.

Answer

The speed of the river current is approximately 19.52 km/h.