Question

Составьте систему уравнений и решите ее: Расстояние между городами 564 км. Навстречу друг другу из городов одновременно вышли поезда и встретились через 6 часов. Скорость одного поезда на 10 км больше скорости другого. Чему равна скорость каждого поезда?

Answer 1

Х - скорость одного
у - скорость другого

{х=10+у         (подставим во второе)
{6х+6у=564

6(10+у)+6у=564
60+6у+6у=564
12у=504
у=504:12
у=42 (км/ч)   (подставим в первое)

х=10+42
х=52 (км/ч)

Ответ: скорость одного поезда 52 км/ч, а другого 42 км/ч

Answer 2

Problem Analysis

We are given the following information: - The distance between two cities is 564 km. - Two trains start from the cities simultaneously and meet after 6 hours. - The speed of one train is 10 km/h greater than the speed of the other train.

We need to find the speed of each train.

Formulating the Equations

Let's assume the speed of the slower train is x km/h. Therefore, the speed of the faster train will be x + 10 km/h.

The distance traveled by the slower train in 6 hours is 6x km, and the distance traveled by the faster train in 6 hours is 6(x + 10) km.

Since the total distance between the two cities is 564 km, we can set up the following equation:

6x + 6(x + 10) = 564

Solving the Equation

Let's solve the equation to find the value of x.

6x + 6(x + 10) = 564

Simplifying the equation:

6x + 6x + 60 = 564

12x + 60 = 564

Subtracting 60 from both sides:

12x = 504

Dividing both sides by 12:

x = 42

Therefore, the speed of the slower train is 42 km/h and the speed of the faster train is 52 km/h.

Answer

The speed of each train is as follows: - Slower train: 42 km/h - Faster train: 52 km/h