Question

Расстояние в 24 км по течению реки катер преодолевает за 2 ч . Найдите скорость течения, если то же расстояние по озеру он может преодолеть за 3 ч. Помогите пожалуйста решить .

Answer 1

1) 24:2=12(км/ч)- скорость катера по течению реки
2)24:3=8(км/ч)-скорость катера
3) 12-8=4(км/ч)

Answer 2

Problem Analysis

We are given that a boat can cover a distance of 24 km downstream in 2 hours and the same distance on a lake in 3 hours. We need to find the speed of the current.

Downstream Speed Calculation

Let's assume the speed of the boat in still water is B km/h and the speed of the current is C km/h. When the boat is moving downstream, the effective speed is the sum of the boat's speed and the speed of the current. Therefore, the boat's downstream speed is B + C km/h.

According to the given information, the boat covers a distance of 24 km downstream in 2 hours. We can use the formula distance = speed × time to calculate the downstream speed:

24 = (B + C) × 2

Upstream Speed Calculation

When the boat is moving upstream against the current, the effective speed is the difference between the boat's speed and the speed of the current. Therefore, the boat's upstream speed is B - C km/h.

According to the given information, the boat covers the same distance of 24 km on the lake in 3 hours. We can use the formula distance = speed × time to calculate the upstream speed:

24 = (B - C) × 3

Solving the Equations

We now have a system of two equations with two unknowns (B and C). We can solve this system of equations to find the values of B and C.

Let's solve the equations:

Equation 1: 24 = (B + C) × 2

Equation 2: 24 = (B - C) × 3

To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of substitution:

From Equation 1, we can express B in terms of C:

B = (24 - 2C) / 2

Substituting this value of B into Equation 2:

24 = ((24 - 2C) / 2 - C) × 3

Simplifying the equation:

24 = (24 - 2C - 2C) × 3

24 = (24 - 4C) × 3

24 = 72 - 12C

12C = 72 - 24

12C = 48

C = 48 / 12

C = 4

Answer

The speed of the current is 4 km/h.

Explanation

The speed of the current is calculated by solving a system of equations. We assume the speed of the boat in still water is B km/h and the speed of the current is C km/h. Using the given information, we set up two equations based on the distances covered downstream and on the lake. By solving these equations, we find that the speed of the current is 4 km/h.