Question

Решите, пожалуйста Катер плив за течією річки 2,2 години і проти течіі 2,8 години.шлях,який катер пройшов проти течіі на 16,4 км більше,ніж шлях,що катер пройшов за течією. Знайти швидкість течіі,якщо власна швидкість катера 44км/год

Answer 1

х - скорость течения реки

44 + х - скорость катера по течению реки

44 - х - скорость катера против течения реки

(44 - х) * 2,8 - (44 + х) * 2,2 = 16,4 

123,2 - 2.,8х - 96,8 - 2,2х = 16,4

123,2 - 96,8 - 16,4 = 2,8х + 2,2х

5х = 10

х = 10 : 5

х = 2 (км/ч) - скорость течения реки

Проверка: 2,8 * (44 - 2) - 2,2 * (44 + 2) = 16,4

                  2,8 * 42 - 2,2 * 46 = 16,4

                  117,6 - 101,2 = 16,4

Ответ: 2 км/ч - скорость течения реки.

Answer 2

Problem Analysis

To solve this problem, we can use the formula:

speed = distance / time

We are given the following information: - Downstream time (with the current) = 2.2 hours - Upstream time (against the current) = 2.8 hours - The boat travels 16.4 km more upstream than downstream - The boat's speed in still water = 44 km/h

Calculations

Let's denote the speed of the current as c and the speed of the boat in still water as b.

1. Downstream speed: - The boat's speed downstream is the sum of the speed of the current and the boat's speed in still water: b + c - Distance downstream = time * speed = 2.2 * (b + c)

2. Upstream speed: - The boat's speed upstream is the difference between the speed of the boat in still water and the speed of the current: b - c - Distance upstream = time * speed = 2.8 * (b - c)

We also know that the distance traveled upstream is 16.4 km more than the distance traveled downstream: - 2.8 * (b - c) = 2.2 * (b + c) + 16.4

Solution

Let's solve the equation to find the speed of the current.

Given: - Boat's speed in still water, b = 44 km/h - Downstream time, t1 = 2.2 hours - Upstream time, t2 = 2.8 hours - Difference in distances, d = 16.4 km

We can solve the equation: - 2.8 * (44 - c) = 2.2 * (44 + c) + 16.4

Let's solve for c.