Question

От станции отошёл поезд со скоростью 62 км/ч. Через 5 часов с той же станции в противоположном направлении вышел другой поезд со скоростью 58 км/ ч. Через какое время после выхода первого поезда расстояние между ними составит 670 км?

Answer 1

62 · 5 = 310 (км) - прошёл первый поезд за 5 часов.
670 - 310 = 360 (км) - расстояние, которое пройдут поезда удаляясь друг от друга.
62 + 58 = 120 (км/ч) - скорость удаления.
360 : 120 = 3 (ч)
3 + 5 = 8 (ч)
Ответ: через 8 часов после выхода первого поезда расстояние между поездами будет 670 км.

Answer 2

Problem Analysis

We are given that a train departs from a station with a speed of 62 km/h. After 5 hours, another train departs from the same station in the opposite direction with a speed of 58 km/h. We need to determine the time it takes for the distance between the two trains to be 670 km.

Solution

Let's break down the problem step by step:

1. Calculate the distance covered by the first train in 5 hours. 2. Calculate the distance covered by the second train in the same amount of time. 3. Determine the total distance covered by both trains. 4. Find the time it takes for the total distance to be 670 km.

Step 1: Calculate the distance covered by the first train in 5 hours

The distance covered by a train can be calculated using the formula: distance = speed × time.

The speed of the first train is 62 km/h, and the time is 5 hours. Therefore, the distance covered by the first train in 5 hours is: distance_1 = speed_1 × time_1 = 62 km/h × 5 h = 310 km.

Step 2: Calculate the distance covered by the second train in 5 hours

The speed of the second train is 58 km/h, and the time is 5 hours. Therefore, the distance covered by the second train in 5 hours is: distance_2 = speed_2 × time_2 = 58 km/h × 5 h = 290 km.

Step 3: Determine the total distance covered by both trains

The total distance covered by both trains is the sum of the distances covered by each train: total_distance = distance_1 + distance_2 = 310 km + 290 km = 600 km.

Step 4: Find the time it takes for the total distance to be 670 km

To find the time it takes for the total distance to be 670 km, we can use the formula: time = distance / speed.

Let's assume the time it takes for the total distance to be 670 km is t hours. The distance covered by the first train in t hours is 62t km, and the distance covered by the second train in t hours is 58t km.

According to the problem, the total distance covered by both trains is 670 km. Therefore, we can write the equation: 62t + 58t = 670.

Simplifying the equation: 120t = 670, t = 670 / 120, t ≈ 5.58 hours.

Therefore, it takes approximately 5.58 hours for the distance between the two trains to be 670 km.

Answer

After the first train departs, it takes approximately 5.58 hours for the distance between the two trains to be 670 km.