Question

Из пунктов А и Б, расстояние между которыми 1020 км, отправились одновременно навстречу друг другу два поезда, причём Скорость одного на 10 км/ч больше скорости другого. Через 5 ч поезда, еще не встретившись, находились на расстоянии 170 км друг от друга. Найдите скорости поездов

Answer 1

1) 1020  - 170 = 850 (км) проехали поезда
2) 850  :  5 = 170 (км/ч) скорость сближения поездов
3) Скорость одного  поезда  х  км/ч , скорость другого поезда  (х - 10) км/ч.
Скорость сближения поездов :  
х  +  (х  - 10)  = 170
х + х  - 10  = 170
2х  - 10  =  170
2х = 170 + 10
2х = 180
х = 180 : 2
х = 90  (км/ч) скорость одного поезда
90  - 10  = 80 (км/ч) скорость другого поезда

Ответ :  90 км/ч  и  80 км/ч .

Answer 2

Problem Analysis

Two trains, A and B, are traveling towards each other from a distance of 1020 km. They started at the same time, and one train is traveling 10 km/h faster than the other. After 5 hours, they were still 170 km apart. We need to find the speeds of the trains.

Given Information

- Distance between the trains, d = 1020 km - Time, t = 5 hours - Distance after 5 hours, d' = 170 km

Solution

Let's denote the speed of train A as v km/h and the speed of train B as v + 10 km/h.

The total distance covered by both trains after 5 hours is the sum of the distances covered by each train: - For train A: 5v - For train B: 5(v + 10)

The sum of these distances is equal to the initial distance minus the distance after 5 hours: - 5v + 5(v + 10) = 1020 - 170

Solving this equation will give us the speeds of the trains.

Calculation

Let's solve the equation: - 5v + 5(v + 10) = 1020 - 170 - 5v + 5v + 50 = 850 - 10v + 50 = 850 - 10v = 800 - v = 80

So, the speed of train A, v, is 80 km/h, and the speed of train B, v + 10, is 90 km/h.

Therefore, the speed of train A is 80 km/h and the speed of train B is 90 km/h.

Final Answer

The speed of train A is 80 km/h and the speed of train B is 90 km/h.