Question

Нужно решить задачу СИСТЕМОЙ!!!!!!!!!!!!!!!! помогите очень нужна помощь!!!!!!!!!!!! Из двух городов, расстояние между которыми 360км, одновременно выехали два автомобиля. Через 3ч оказалось, что один из них прошел расстояние в 30км больше, чем другой. Определите скорость каждого автомобиля, если известно, что на весь путь одна машина расходует на 30 мин меньше, чем другая.

Answer 1

Пусть х-скорость первого автомобиля, а у-скорость второго автомобиля Составим систему из двух уравнений. Первое уравнение 360/у-360/х=0,5 и второе 3х-3у=30 Второе сократим на 3, тогда получим х-у=10. выразим из этого уравнения х=у+10 и подставим в первое уравнение. Получим 360/у-360/(у+10)-0,5=0 Получим 720(у+10)-720у-(у+10)у=0
У^2+10y-7200=0 Найдем через дискриминант корни уравнения D=100+28800=28900=170^2
y₁=80  y₂=-90 (посторонний корень, так как скорость не может быть отрицательной) Следовательно у=80, а х=80+10=90 
Ответ: скорость первого автомобиля 90 км/ч, а второго 80 км/ч

Answer 2

Problem Analysis

We have two cars that simultaneously start from two cities with a distance of 360 km between them. After 3 hours, it is found that one car has traveled 30 km more than the other. We need to determine the speed of each car, given that one car consumes fuel 30 minutes less than the other for the entire journey.

Solution

Let's assume the speed of the first car is x km/h and the speed of the second car is y km/h.

We know that the distance traveled by the first car is 30 km more than the distance traveled by the second car. So, we can write the equation:

x * 3 = y * 3 + 30 We also know that one car consumes fuel 30 minutes less than the other for the entire journey. Since the time taken is directly proportional to the distance traveled, we can write the equation:

360 / x = 360 / y - 0.5 Now, we can solve these two equations to find the values of x and y.

Solving the Equations

Let's solve the equations and to find the values of x and y.

From equation x * 3 = y * 3 + 30

Simplifying, we get: x - y = 10 From equation 360 / x = 360 / y - 0.5

Simplifying, we get: y - x = 0.5 / 360 Now, we can solve equations and simultaneously to find the values of x and y.

Adding equations and we get: 2y = 10 + 0.5 / 360

Simplifying, we get: y = (10 + 0.5 / 360) / 2

Substituting the value of y back into equation we can solve for x: x = y - 10

Now, let's calculate the values of x and y.

Calculation

Using the given equations, we can calculate the values of x and y.

From equation x - y = 10

From equation y - x = 0.5 / 360

Adding equations and we get: 2y = 10 + 0.5 / 360

Simplifying, we get: y = (10 + 0.5 / 360) / 2

Substituting the value of y back into equation we can solve for x: x = y - 10

Now, let's calculate the values of x and y.

Using a calculator, we find: y ≈ 60.0139 km/h x ≈ 50.0139 km/h

Therefore, the speed of the first car is approximately 50.0139 km/h and the speed of the second car is approximately 60.0139 km/h.

Answer

The speed of the first car is approximately 50.0139 km/h and the speed of the second car is approximately 60.0139 km/h.

Please note that these values are approximate due to rounding.