Question

катер проплыл определенное расстояние по течению реки за 1,6 часа а против течения за 2, 4 часа Найдите скорость катера в стоячей воде если скорость течения реки 2,5 км/ч Ребята пожалуйста помогите мне оооочень срочно 44 бала

Answer 1

Пусть х - скорость катера в стоячей воде.
Тогда:
х+2,5 - скорость катера, плывущего по течению;
х-2,5 - скорость катера, плывущего против течения.
1,6(х+2,5) - расстояние, пройденное катером по течению;
2,4(х-2,5) - расстояние, пройденное катером против течения.
Поскольку против течения и по течению катер прошел одинаковое расстояние, то:
1,6(х+2,5) = 2,4(х-2,5)
Разделим обе части уравнения ня
0,8:
2(х+2,5) = 3(х-2,5)
2х + 5 = 3х - 7,5
3х-2х = 5+7,5
х = 12,5 км/ч - скорость катера в стоячей воде.
Ответ: 12,5 км/ч

Answer 2

Problem Analysis

We are given that a boat traveled a certain distance with the current of a river in 1.6 hours and against the current in 2.4 hours. We need to find the speed of the boat in still water, given that the speed of the current is 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, the effective speed is the sum of the boat's speed and the speed of the current. So, the boat's effective speed is (x + 2.5) km/h.

When the boat is traveling against the current, the effective speed is the difference between the boat's speed and the speed of the current. So, the boat's effective speed is (x - 2.5) km/h.

We can use the formula distance = speed × time to calculate the distance traveled in both cases.

1. When the boat is traveling with the current: - Distance = (x + 2.5) km/h × 1.6 hours

2. When the boat is traveling against the current: - Distance = (x - 2.5) km/h × 2.4 hours

Since the distance traveled in both cases is the same, we can set up the following equation:

(x + 2.5) × 1.6 = (x - 2.5) × 2.4

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

Calculation

Expanding the equation:

1.6x + 4 = 2.4x - 6

Rearranging the terms:

2.4x - 1.6x = 4 + 6

Simplifying:

0.8x = 10

Dividing both sides by 0.8:

x = 10 / 0.8

Calculating:

x = 12.5

Answer

The speed of the boat in still water is 12.5 km/h.

Verification

Let's verify our answer by substit