Question

(2 бали). Катер плив за течією річки 2,2 год і проти течії. 2,8 год. Шлях, який катер пройшов проти течії, на 16,4 км довший, ніж шлях, що пройшов катер за те- чією. Знайдіть швидкість течії, якщо власна швид- кість катера становить 44 км/год.​

Answer 1

Объяснение:

Скорость течения = х км/ч

Скорость катера по течению = 44 + х км/ч

Скорость катера против течения = 44 - х км/ч

2,8*(44 - х) - 2,2*(44 + х) = 16,4

123,2 - 2,8х - 96,8 - 2,2х = 16,4

-5х + 26,4 = 16,4

-5х = 16,4 - 26,4

-5х = -10

х = -10 : (-5)

х = 2

Скорость течения = (х) = 2 км/ч

Answer 2

Ответ:

Объяснение:

Нехай швидкість течії x, тоді швидкість катера за течією 44+x, а проти течії 44-x. Складемо рівняння:

2.2*(44+x)+16.4=2.8*(44-x)

96.8+2.2x+16.4=123.2-2.8x

5x=10

x=2

Відповідь: швидкість течії 2км/год

Answer 3

Problem Analysis

We are given that a boat travels downstream for 2.2 hours and upstream for 2.8 hours. The distance traveled upstream is 16.4 km longer than the distance traveled downstream. We need to find the speed of the current, given that the boat's speed is 44 km/h.

Solution

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

When the boat is traveling downstream, the effective speed is the sum of the boat's speed and the speed of the current. So the distance traveled downstream can be calculated as:

Distance downstream = (Boat's speed + Current's speed) × Time downstream

Similarly, when the boat is traveling upstream, the effective speed is the difference between the boat's speed and the speed of the current. So the distance traveled upstream can be calculated as:

Distance upstream = (Boat's speed - Current's speed) × Time upstream

We are given that the boat's speed is 44 km/h, the time downstream is 2.2 hours, and the time upstream is 2.8 hours. We also know that the distance traveled upstream is 16.4 km longer than the distance traveled downstream.

Using the above equations, we can set up the following system of equations:

Equation 1: Distance downstream = (44 + x) × 2.2 Equation 2: Distance upstream = (44 - x) × 2.8 Equation 3: Distance upstream = Distance downstream + 16.4

We can solve this system of equations to find the value of x, which represents the speed of the current.

Let's solve the equations step by step:

From Equation 1, we have: Distance downstream = 2.2(44 + x)

From Equation 2, we have: Distance upstream = 2.8(44 - x)

From Equation 3, we have: 2.8(44 - x) = 2.2(44 + x) + 16.4

Now, let's solve for x:

2.8(44 - x) = 2.2(44 + x) + 16.4 123.2 - 2.8x = 96.8 + 2.2x + 16.4 123.2 - 96.8 - 16.4 = 2.2x + 2.8x 10 = 5x x = 2

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

Answer

The speed of the current is 2 km/h.