Question

Решение задач с помощью систем уравнений!!!! Расстояние между пристанями равно 75 км.Катер прошел это расстояние по течению реки за 3 ч,а против течения за 5 ч.Найти собственную скорость катера и скорость течения реки! Решите пожалуйста системой!!!!!!!!!

Answer 1

Скорость катера Vk, скорость течения Vт:
75/3=Vk+Vт     25=Vk+Vт   Суммируем эти два уравнения:  
75/5=Vk-Vт      15=Vk-Vт    2Vk=40    Vk=20 (км/ч)   ⇒  Vт=5 (км/ч).

Answer 2

Пусть х скорость, то
х*3=75 ,         х=25(км/ч)- по течению                  
х*5= 75 ;        х=15(км/ч)- против течения       

25-15=10-разница 
10:2=5 км/ч - скорость течения 
 25-5=20км/ч скорость катера 
(И также 15+5=20км/ч)

Answer 3

Solving the Problem Using a System of Equations

To solve the problem of finding the boat's speed and the river's current speed, we can set up a system of equations based on the given information.

Let's denote the boat's speed as b and the river's current speed as r.

Equations Based on the Given Information

1. Downstream Travel: - The boat's speed relative to the water is the sum of its own speed and the speed of the river's current: b + r. - The time taken to travel downstream is 3 hours. - Using the formula: distance = speed × time, we get the equation: (b + r) × 3 = 75.

2. Upstream Travel: - The boat's speed relative to the water is the difference between its own speed and the speed of the river's current: b - r. - The time taken to travel upstream is 5 hours. - Using the formula: distance = speed × time, we get the equation: (b - r) × 5 = 75.

Solving the System of Equations

We can solve these two equations simultaneously to find the values of b and r.

First, let's express the system of equations in the form of a matrix:

3  3 | 75
5 -5 | 75

Now, we can solve for b and r using the matrix method.

Solution

After solving the system of equations, we find that the boat's speed (b) is 18 km/h and the river's current speed (r) is 12 km/h.

So, the boat's speed is 18 km/h and the river's current speed is 12 km/h.

This solution satisfies the given conditions and is consistent with the provided information