Question

Речной корабль прошёл по течению реки 24 км за 2 ч, а на обратный путь у него ушло 3 ч. Найди скорость движения корабля в стоячей воде и скорость течения реки. (Ответы должны быть 2км/ч и 10км/ч! А как решить я не понимаю!! Помогите пожалуйста!)

Answer 1

Ответ:

Vкатера = 10 км/ч

Vреки = 2 км/ч

Пошаговое объяснение:

Vкатера + Vреки = 24:2 = 12 (км/ч)

Vкатера - Vреки = 24:3 = 8 (км/ч)

Складываем два этих уравнения и получаем:

Vкатера + Vреки + Vкатера - Vреки = 12 + 8

2 * Vкатера = 20

Vкатера = 20 : 2 = 10 (км/ч) - скорость катера в стоячей воде

12-10 = 2 (км/ч) - скорость течения реки

Проверка:

(10 + 2) * 2 = 24 (км) - верно

(10-2)*3 = 24 (км) - верно

Answer 2

Problem Analysis

We are given that a riverboat traveled downstream for 24 km in 2 hours and then returned upstream in 3 hours. We need to find the speed of the boat in still water and the speed of the river current.

Let's assume the speed of the boat in still water is x km/h and the speed of the river current is y km/h.

Downstream Journey

During the downstream journey, the boat's speed is increased by the speed of the river current. So, the effective speed of the boat is (x + y) km/h.

The distance traveled downstream is 24 km, and the time taken is 2 hours. We can use the formula distance = speed × time to write the equation:

24 = (x + y) × 2

Upstream Journey

During the upstream journey, the boat's speed is decreased by the speed of the river current. So, the effective speed of the boat is (x - y) km/h.

The distance traveled upstream is also 24 km, and the time taken is 3 hours. We can use the same formula to write the equation:

24 = (x - y) × 3

Solving the Equations

We now have a system of two equations with two variables. We can solve these equations simultaneously to find the values of x and y.

Let's solve the equations:

From equation 24 = 2x + 2y From equation 24 = 3x - 3y To eliminate the variable y, we can multiply equation by 3 and equation by 2:

3 × (24) = 3 × (2x + 2y) 72 = 6x + 6y 2 × (24) = 2 × (3x - 3y) 48 = 6x - 6y Adding equations and eliminates the variable y:

72 + 48 = 6x + 6y + 6x - 6y 120 = 12x

Dividing both sides by 12, we get:

x = 10

Substituting the value of x into equation we can find the value of y:

24 = 2(10) + 2y 24 = 20 + 2y 2y = 24 - 20 2y = 4 y = 2

Solution

The speed of the boat in still water is 10 km/h, and the speed of the river current is 2 km/h.

I hope this helps! Let me know if you have any further questions.