Question

Помогите пожалуйста таблицей прошуу дам 15 баллов Теплоход прошел 4 ч по течению реки и 3 ч против течения. Путь, пройденный теплоходом по течению, на 48 км больше пути, пройденного против течения. Найдите скорость теплохода в стоячей воде, если скорость течения равна 2,5 км\4

Answer 1

Problem Analysis

To solve this problem, we need to find the speed of the boat in still water. We are given that the boat traveled for 4 hours with the current and 3 hours against the current. The distance traveled with the current is 48 km more than the distance traveled against the current. The speed of the current is given as 2.5 km/h.

Solution

Let's assume the speed of the boat in still water 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. So, the effective speed is (x + 2.5) km/h.

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. So, the effective speed is (x - 2.5) km/h.

We are given that the boat traveled for 4 hours with the current and 3 hours against the current. The distance traveled with the current is 48 km more than the distance traveled against the current.

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

1. Distance traveled with the current: (x + 2.5) × 4 = D 2. Distance traveled against the current: (x - 2.5) × 3 = D - 48

Simplifying these equations, we get: 1. 4x + 10 = D 2. 3x - 7.5 = D - 48

We can solve these equations simultaneously to find the value of x.

Let's solve the equations:

4x + 10 = 3x - 7.5 + 48

Simplifying further:

4x + 10 = 3x + 40.5

4x - 3x = 40.5 - 10

x = 30.5

Therefore, the speed of the boat in still water is 30.5 km/h.

Answer

The speed of the boat in still water is 30.5 km/h.