Question

Пассажирский и товарный поезд вышли в одном направлении одновременно с двух станций, расстояние между которыми 512км. Скорость пассажирского поезда была в 2 раза быстрее скорости товарного и через 8ч после выхода пассажирский поезд догнал товарный. С какими скоростями они шли?

Answer 1

1) 512:8=64(км/ч)- скорость сближения
2) 64:2=32(км/ч)
ответ: скорость 1- 64, 2-32

Answer 2

Problem Analysis

We are given that a passenger train and a freight train departed from two different stations in the same direction at the same time. The distance between the two stations is 512 km. The passenger train was traveling at twice the speed of the freight train. After 8 hours, the passenger train caught up with the freight train. We need to find the speeds of both trains.

Solution

Let's assume the speed of the freight train is x km/h. Since the passenger train is traveling at twice the speed of the freight train, its speed will be 2x km/h.

We know that distance = speed × time.

For the passenger train: - Distance = 512 km - Speed = 2x km/h - Time = 8 hours

For the freight train: - Distance = 512 km - Speed = x km/h - Time = 8 hours

Using the formula distance = speed × time, we can set up the following equations:

Passenger train: 512 = (2x) × 8

Freight train: 512 = x × 8

Simplifying the equations:

Passenger train: 512 = 16x

Freight train: 512 = 8x

Now, we can solve these equations to find the values of x and 2x.

From the equation 512 = 16x, we can divide both sides by 16 to get:

x = 512 / 16 = 32

Therefore, the speed of the freight train is 32 km/h.

Substituting this value back into the equation 512 = 8x, we can find the speed of the passenger train:

512 = 8x 512 = 8 * 32 512 = 256

Therefore, the speed of the passenger train is 64 km/h.

Answer

The passenger train was traveling at a speed of 64 km/h and the freight train was traveling at a speed of 32 km/h.