Question

Решите задачу с помощью уравнения:Катер прошел 5 часов по течению и 8 часов против течения. Скорость течения реки 3 км/ч. Найдите скорость катера и весь путь, если по течению и против пройдено одинаковое расстояние, решите пожалуйста даю 50 баллов

Answer 1

Ответ:

В решении.

Пошаговое объяснение:

Решить задачу с помощью уравнения:

Катер прошел 5 часов по течению и 8 часов против течения. Скорость течения реки 3 км/ч. Найдите скорость катера и весь путь, если по течению и против пройдено одинаковое расстояние.

Формула движения: S=v*t  

S - расстояние            v - скорость             t – время

х - собственная скорость катера;

х + 3 - скорость по течению;

х - 3 - скорость против течения;

5(х + 3) - путь по течению;

8(х - 3) - путь против течения;

Расстояние одно и то же по условию, уравнение:

5(х + 3) = 8(х - 3)

Раскрыть скобки:

5х + 15 = 8х - 24

5х - 8х = -24 - 15

-3х = -39

х = -39/-3  (деление)

х = 13 (км/час) - собственная скорость катера;

5*(13 + 3) = 5*16 = 80 (км) - весь путь.

Проверка:

8*(13 - 3) = 8*10 = 80 (км), верно.

Answer 2

Problem Statement:

We are given that a boat traveled for 5 hours with the current and 8 hours against the current. The speed of the current is 3 km/h. We need to find the speed of the boat and the total distance traveled, assuming that the boat traveled the same distance in both directions.

Solution:

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

When the boat is traveling with the current, its effective speed is the sum of its own speed and the speed of the current. So, the effective speed is (x + 3) km/h.

When the boat is traveling against the current, its effective speed is the difference between its own speed and the speed of the current. So, the effective speed is (x - 3) km/h.

We know that the boat traveled for 5 hours with the current and 8 hours against the current.

Using the formula distance = speed × time, we can set up the following equations:

1. Distance traveled with the current: (x + 3) × 5 2. Distance traveled against the current: (x - 3) × 8

Since the boat traveled the same distance in both directions, we can set up the equation:

(x + 3) × 5 = (x - 3) × 8

Now, let's solve this equation to find the value of x.

Expanding the equation:

5x + 15 = 8x - 24

Rearranging the terms:

8x - 5x = 15 + 24

Simplifying:

3x = 39

Dividing both sides by 3:

x = 13

Therefore, the speed of the boat is 13 km/h.

To find the total distance traveled, we can substitute the value of x into one of the equations:

Distance traveled with the current: (13 + 3) × 5 = 16 × 5 = 80 km

Therefore, the total distance traveled by the boat is 80 km.

So, the speed of the boat is 13 km/h and the total distance traveled is 80 km.

Let me know if you need any further assistance!