Question

С железнодорожной станции одновременно в противоположных направлениях вышли два поезда и через 3,4 часа оказались на расстоянии 550,8 км друг от друга. Найдите скорости поездов, если известно, что скорость одного из них в 1,25 раза меньше скорости другого.

Answer 1

1) 550,8 : 3,4 = 162 км/ч скорость удаления поездов
2) 1 + 1,25 = 2,25 части в скорость 162 км/ч
3) 162 : 2,25 = 72 км/ч скорость одного поезда
4) 72 * 1,25 = 90 км/ч скорость второго поезда

Answer 2

Problem Analysis

We are given that two trains leave a railway station simultaneously in opposite directions. After 3.4 hours, they are 550.8 km apart. We need to find the speeds of the trains, given that the speed of one train is 1.25 times smaller than the speed of the other train.

Solution

Let's assume the speed of the faster train is x km/h. Then the speed of the slower train will be 1.25x km/h.

We can use the formula distance = speed × time to calculate the distances covered by each train in 3.4 hours.

For the faster train: distance = speed × time distance = x × 3.4

For the slower train: distance = speed × time distance = 1.25x × 3.4

According to the problem, the sum of the distances covered by both trains is 550.8 km. So we can write the equation:

x × 3.4 + 1.25x × 3.4 = 550.8

Simplifying the equation:

3.4x + 4.25x = 550.8

7.65x = 550.8

x = 550.8 / 7.65

x ≈ 71.96

Therefore, the speed of the faster train is approximately 71.96 km/h, and the speed of the slower train is approximately 1.25 times smaller, which is approximately 57.57 km/h.

Answer

The speed of the faster train is approximately 71.96 km/h, and the speed of the slower train is approximately 57.57 km/h.