Question

решите задачу системы линейных уравнений с двумя переменными способом подстановки.сумма скорости катера по течению и скорости против течения равна 44 км/ч. катер проплывает по течению за 5 ч такое же расстояние,какое он проплывает против течения за 6ч.найдите скорость катера по течению и скорость cпротив течения. .

Answer 1

Х-собств. скорость катера,

У-скорость течения

х+у-скорость по течению

х-у-скорость против течения

система уравнений:

х+у-х-у=44

5(х+у)=6(х-у)

Расскроем скобки, упростим:

2х=44

-х+11у=0

Найдем х из первого уравн. х=44:2=22,подставим во второе уравнение

-22+11у=0

У=22:11=2

 скорость катера по течению 22+2=24 кмв ч,против течения 22-2=20 км в час

Answer 2

Problem:

We are given a system of linear equations with two variables. The sum of the boat's speed with the current and the speed against the current is 44 km/h. The boat travels a certain distance with the current in 5 hours, which is the same distance it travels against the current in 6 hours. We need to find the speed of the boat with the current and the speed against the current.

Solution:

Let's assume the speed of the boat with the current is x km/h, and the speed against the current is y km/h.

From the given information, we can form the following equations:

Equation 1: x + y = 44 (the sum of the boat's speed with the current and the speed against the current is 44 km/h)

Equation 2: 5x = 6y (the boat travels a certain distance with the current in 5 hours, which is the same distance it travels against the current in 6 hours)

To solve this system of equations using the method of substitution, we can solve Equation 2 for x and substitute it into Equation 1.

From Equation 2, we have x = (6/5)y. Substituting this into Equation 1, we get:

(6/5)y + y = 44

Simplifying the equation, we have:

(11/5)y = 44

To solve for y, we can multiply both sides of the equation by (5/11):

y = (44 * 5) / 11

Simplifying further, we find:

y = 20

Now, we can substitute the value of y back into Equation 2 to find x:

5x = 6 * 20

Simplifying, we have:

5x = 120

Dividing both sides of the equation by 5, we find:

x = 24

Therefore, the speed of the boat with the current is 24 km/h, and the speed against the current is 20 km/h.

Answer:

The speed of the boat with the current is 24 km/h, and the speed against the current is 20 km/h.