Question

С двух железнодорожных станций, расстояние между которыми 124 км, одновременно в противоположных направлениях отправились два поезда. Через 1 ч 45 мин расстояние между поездами стало ровно 369 км. отношение скорости первого поезда к скорости второго равно 3:2 найдите скорость

Answer 1

1) 1 45\60 = 1.75 часа
2) 369 - 124 = 245 км
3) 245 = 1.75 * V общая ---> V общая = 245 : 1.75 = 140 (км\час)
4) 140 : ( 3 + 2 ) = 140 : 5 = 28 (км\час) - 1 часть
5) Скорость первого поезда
28 * 3 = 84 ( км\час)
6) Скорость второго поезда
28 * 2 = 56 (км\час)

Answer 2

1)369-124=245 км проехали поезда за 1 час 45 мин
2)3+2=5 частей общая скорость
3) 245:1,75= 140 км/час общая скорость  (1,75 это 1час45 мин перевели в часы)
4)140:5=28 км/час приходится на одну часть
5)3*28= 84 км/час скорость первого
6)2*28= 56 км/час скорость второго

Answer 3

Problem Analysis

We are given that two trains start simultaneously from two railway stations that are 124 km apart in opposite directions. After 1 hour and 45 minutes, the distance between the trains becomes 369 km. We are also given that the ratio of the speed of the first train to the speed of the second train is 3:2. We need to find the speed of the trains.

Solution

Let's assume the speed of the first train is 3x and the speed of the second train is 2x, where x is a constant.

We can calculate the time taken by the first train to cover the distance of 369 km using the formula: time = distance / speed. The time taken by the first train is (124 + 369) / (3x) = 493 / (3x).

Similarly, the time taken by the second train to cover the distance of 369 km is (369 - 124) / (2x) = 245 / (2x).

According to the given information, the time taken by both trains is 1 hour and 45 minutes, which is equal to 1.75 hours.

So, we can set up the equation: 493 / (3x) + 245 / (2x) = 1.75

To solve this equation, we can multiply both sides by 6x to eliminate the denominators: 6x * (493 / (3x) + 245 / (2x)) = 6x * 1.75 (6 * 493) / 3 + (6 * 245) / 2 = 10.5x (2 * 493) + (3 * 245) = 10.5x 986 + 735 = 10.5x 1721 = 10.5x x = 1721 / 10.5

Now, we can calculate the speed of the first train: Speed of the first train = 3x = 3 * (1721 / 10.5)

Finally, we can calculate the speed of the second train: Speed of the second train = 2x = 2 * (1721 / 10.5)

Let's calculate the speeds of the trains.

Calculation

Speed of the first train: Speed of the first train = 3 * (1721 / 10.5) = 5163 / 10.5 = 492

Speed of the second train: Speed of the second train = 2 * (1721 / 10.5) = 3442 / 10.5 = 328

Answer

The speed of the first train is 492 km/h and the speed of the second train is 328 km/h.