Question

Ребят помогите пожалуйста Из пункта А в пункт В , расстояние между которыми 300 км выехал автомобиль.Через 30 мин выехал другой автомобиль. Через 2 часа автомобили встретились. Найдите скорости автомобилей , если известно , что , выехав одновременно , автомобили встретились бы через 2 2/9 часа.

Answer 1

Считаю, что второй авто выехал на встречу первому.
30мин=30/60ч=0,5ч

300:2 2/9=300:20/9=300*9/20=30*9/2=15*9=135 км/ч-скорость сближения
х-скорость первого
135-х-скорость второго

0,5х+135*2=300
0,5х+270=300
0,5х=30
х=30/0,5=300/5=60 км/ч-скорость первого
135-60=75 км/ч-скорость второго

Answer 2

Problem Analysis

We are given that two cars start from point A and point B, which are 300 km apart. One car starts 30 minutes before the other. After 2 hours, the cars meet each other. We need to find the speeds of the cars.

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 in 2 hours is 2x km, and the distance traveled by the second car in 2 hours is 2y km.

Since the cars meet each other after 2 hours, the total distance traveled by both cars is equal to the distance between point A and point B, which is 300 km.

So, we can write the equation: 2x + 2y = 300.

We also know that the first car started 30 minutes (0.5 hours) before the second car. Therefore, the first car traveled for 2 hours + 0.5 hours = 2.5 hours, while the second car traveled for 2 hours.

We are given that if the cars had started at the same time, they would have met after 2 2/9 hours. So, we can write another equation: 2.5x + 2y = 2 2/9 * (x + y).

Now, we have a system of two equations with two variables. We can solve this system to find the values of x and y.

Solving the System of Equations

To solve the system of equations, we can use substitution or elimination method. Let's use the elimination method.

Multiplying the first equation by 2/9, we get: (4/9)x + (4/9)y = 100/3.

Subtracting this equation from the second equation, we get: 2.5x + 2y - (4/9)x - (4/9)y = 2 2/9 * (x + y) - 100/3.

Simplifying the equation, we get: (22/9)x + (14/9)y = 200/9.

Now, we have a new equation: (22/9)x + (14/9)y = 200/9.

Multiplying the first equation by 14/9, we get: (28/9)x + (28/9)y = 1400/9.

Subtracting this equation from the new equation, we get: (22/9)x + (14/9)y - (28/9)x - (28/9)y = 200/9 - 1400/9.

Simplifying the equation, we get: -(6/9)x = -1200/9.

Simplifying further, we get: -(2/3)x = -400/3.

Dividing both sides by -(2/3), we get: x = (400/3) / (2/3).

Simplifying, we get: x = 200.

Now, we can substitute the value of x into the first equation to find the value of y.

Substituting x = 200 into the equation 2x + 2y = 300, we get: 2(200) + 2y = 300.

Simplifying, we get: 400 + 2y = 300.

Subtracting 400 from both sides, we get: 2y = -100.

Dividing both sides by 2, we get: y = -50.

Since speed cannot be negative, we discard the negative value of y.

Therefore, the speed of the first car is 200 km/h and the speed of the second car is 50 km/h.

Answer

The speed of the first car is 200 km/h and the speed of the second car is 50 km/h.