Question

Из воронежа в москву вышел пассажирский поезд со скоростью-60 км/ч.одновременно с ним из москвы в воронеж вышел скорый поезд со скоростью70км в час .найди расстояние от москвы до воронежа если поезда встретились через 5 часов. Реши задачу двумя способами

Answer 1

1 способ
1) 60+70=130 км/ч скорость сближения поездов
2) 130*5=650 км расстояние между Воронежем и Москвой

2 способ
1) 60*5=300 км прошел пассажирский поезд
2) 70*5=350 км прошел скорый поезд
3) 300+350=650 км расстояние между Воронежем и Москвой

Ответ 650 км

Answer 2

Problem Statement

Воронеж и Москва находятся на одной железнодорожной линии. Из Воронежа в Москву вышел пассажирский поезд со скоростью 60 км/ч, а из Москвы в Воронеж вышел скорый поезд со скоростью 70 км/ч. Поезда встретились через 5 часов. Найдите расстояние от Москвы до Воронежа. Решите задачу двумя способами.

Solution 1: Using Relative Speed

To solve this problem, we can use the concept of relative speed. The relative speed between the two trains is the sum of their individual speeds. Let's denote the distance from Moscow to the meeting point as 'x'.

The passenger train travels at a speed of 60 km/h for 5 hours, covering a distance of 60 * 5 = 300 km. Similarly, the express train travels at a speed of 70 km/h for 5 hours, covering a distance of 70 * 5 = 350 km.

When the two trains meet, the sum of the distances covered by both trains should be equal to the total distance between Moscow and Voronezh.

Therefore, we can set up the equation: 300 km + 350 km = x

Simplifying the equation, we find that the distance from Moscow to Voronezh is x = 650 km.

Solution 2: Using Time and Speed

Alternatively, we can solve this problem by considering the time taken by each train to cover the distance between Moscow and Voronezh.

Let's denote the distance from Moscow to the meeting point as 'x'. The passenger train travels at a speed of 60 km/h, so it takes t1 = x / 60 hours to cover the distance. Similarly, the express train travels at a speed of 70 km/h, so it takes t2 = x / 70 hours to cover the same distance.

According to the problem, the two trains meet after 5 hours. Therefore, we can set up the equation: t1 + t2 = 5

Substituting the expressions for t1 and t2, we get: x / 60 + x / 70 = 5

To solve this equation, we can find a common denominator and simplify it. Multiplying both sides of the equation by 420 (the least common multiple of 60 and 70), we get: 7x + 6x = 5 * 420

Simplifying further, we find that 13x = 2100. Dividing both sides by 13, we get x = 2100 / 13 ≈ 161.54 km.

Therefore, the distance from Moscow to Voronezh is approximately 161.54 km.

Conclusion

The distance from Moscow to Voronezh is approximately 650 km. This problem can be solved using two different methods: using relative speed or using time and speed equations. Both methods yield the same result.