Question

Лодка плыла 1,8 ч. По течению, и 2,6 ч против течения. Путь, который проплыла лодка против течения, оказался на 6 км больше чем тот, когда она плыла по течению. найдите скорость течения реки, если скорость лодки равна 24км/я в стоячей воде

Answer 1

Х - скорость течения реки.
24 + х - скорость лодки по течению.
24 - х - скорость лодки против течения.
2,6 (24 - х) - расстояние, которое проплыла лодка против течения.
1,8(24 + х) - расстояние по течению .

2,6(24 -х) - 1,8(24,+х) = 6
62,4 - 2,6х - 43,2 - 1,8х = 6
-2,6х - 1,8х = 6 - 62,4 + 43.2
-4,4х = -13,2
х = 3 км/ч - скорость течения реки.

Answer 2

Problem Analysis

We are given that a boat traveled for 1.8 hours with the current and 2.6 hours against the current. The distance traveled against the current was 6 km more than the distance traveled with the current. We need to find the speed of the river's current, given that the speed of the boat in still water is 24 km/h.

Solution

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

When the boat is traveling with the current, its effective speed is the sum of the speed of the boat in still water and the speed of the current. Therefore, the distance traveled with the current can be calculated as:

Distance with current = (Speed of boat + Speed of current) × Time with current

When the boat is traveling against the current, its effective speed is the difference between the speed of the boat in still water and the speed of the current. Therefore, the distance traveled against the current can be calculated as:

Distance against current = (Speed of boat - Speed of current) × Time against current

We are given that the distance traveled against the current is 6 km more than the distance traveled with the current. Therefore, we can write the equation:

Distance against current = Distance with current + 6

Substituting the formulas for distance with current and distance against current, we get:

(Speed of boat - Speed of current) × Time against current = (Speed of boat + Speed of current) × Time with current + 6

Now, we can substitute the given values: - Speed of boat = 24 km/h - Time with current = 1.8 hours - Time against current = 2.6 hours

Simplifying the equation will allow us to solve for the speed of the river's current.

Calculation

Let's calculate the speed of the river's current using the equation derived above.

Equation: (Speed of boat - Speed of current) × Time against current = (Speed of boat + Speed of current) × Time with current + 6

Substituting the given values: (24 - x) × 2.6 = (24 + x) × 1.8 + 6

Simplifying the equation: 62.4 - 2.6x = 43.2 + 1.8x + 6

Combining like terms: 62.4 - 43.2 - 6 = 2.6x + 1.8x

Simplifying further: 13.2 = 4.4x

Dividing both sides by 4.4: x = 13.2 / 4.4

Calculating the value: x = 3

Answer

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