Question

Катер, собственная скорость которого 8км\ч, прошел по реке расстояние равное 15 км по течению и такое же растояние против течения. Найди скорость течения реки, если время, затраченное на весь путь, равно 4 часа

Answer 1

Cкорость течения реки = х (км/ч)
Скорость катера по течению реки = (8 + х ) км/ч
Скорость катера против течения = (8 - х) км/ч
Время по течению реки = 15/ (8 + х) ч
Время против течения реки = 15/ (8 -х) ч
Уравнение:
15 / (8 + х) + 15/(8 - х) = 4
15 * (8 - х) + 15 * (8 + х) = 4 * (8^2 - x^2)
256 - 4x^2 = 120 - 15x + 120 + 15x
- 4x^2 +  256 - 240 = 0
  4x^2 = 16
   x^2 = 4
  x = 2
Ответ: 2км/ч - скорость течения реки.

Answer 2

Problem Statement

A boat with a speed of 8 km/h traveled a distance of 15 km downstream and the same distance upstream on a river. The total time taken for the entire journey was 4 hours. We need to find the speed of the river's current.

Solution

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

To solve this problem, we can use the formula: distance = speed × time.

# Downstream Journey

During the downstream journey, the boat's speed is the sum of its own speed and the speed of the river's current. So, the effective speed of the boat during the downstream journey is (8 + x) km/h.

The distance traveled downstream is 15 km.

Using the formula, we can calculate the time taken for the downstream journey as follows: 15 km = (8 + x) km/h × t1.

# Upstream Journey

During the upstream journey, the boat's speed is the difference between its own speed and the speed of the river's current. So, the effective speed of the boat during the upstream journey is (8 - x) km/h.

The distance traveled upstream is also 15 km.

Using the formula, we can calculate the time taken for the upstream journey as follows: 15 km = (8 - x) km/h × t2.

# Total Time

The total time taken for the entire journey is given as 4 hours.

So, we have the equation: t1 + t2 = 4.

Now, we have two equations with two unknowns. We can solve these equations to find the value of x, the speed of the river's current.

Let's solve the equations:

From the equation for the downstream journey: 15 = (8 + x) × t1. (Equation 1)

From the equation for the upstream journey: 15 = (8 - x) × t2. (Equation 2)

We can rewrite Equation 1 as: t1 = 15 / (8 + x).

We can rewrite Equation 2 as: t2 = 15 / (8 - x).

Substituting these values into the equation for the total time, we get:

15 / (8 + x) + 15 / (8 - x) = 4.

Simplifying this equation will give us the value of x, the speed of the river's current.

Let's solve the equation:

15 / (8 + x) + 15 / (8 - x) = 4.

Multiplying both sides of the equation by (8 + x)(8 - x) to eliminate the denominators, we get:

15(8 - x) + 15(8 + x) = 4(8 + x)(8 - x).

Simplifying further, we have:

120 - 15x + 120 + 15x = 4(64 - x^2).

Simplifying again, we get:

240 = 256 - 4x^2.

Rearranging the equation, we have:

4x^2 = 256 - 240.

Simplifying further, we get:

4x^2 = 16.

Dividing both sides of the equation by 4, we have:

x^2 = 4.

Taking the square root of both sides of the equation, we get:

x = ±2.

Since the speed of the river's current cannot be negative, we can conclude that the speed of the river's current is 2 km/h.

Therefore, the speed of the river's current is 2 km/h.

Answer

The speed of the river's current is 2 km/h.