Question

Из двух городов расстояние между которыми 1887км в разное время выехали два поезда. К тому времени, когда второй поезд выехал из своего города, первый успел проехать 510км. Встреча произошла через 9ч после выхода второго поезда. Скорость первого поезда в 2 раза больше скорости второго поезда. Найдите расстояние между поездами через 3часа после встречи, если, встретившись, они продолжили свой путь без остановки.

Answer 1

1) 1887км - 510км = 1377км - осталось пройти поездам до встречи

2) 1377км : 9ч = 153км/ч - скорость сближения поездов

3) 153км/ч : 3 = 51км/ч - скорость 2-го поезда

4) 51км/ч · 2 = 102км/ч - скорость 1-го поезда

5) 153км/ч · 3ч = 459км - расстояние между поездами через 3 часа после встречи

Ответ: 459км

Answer 2

Problem Analysis

We are given that the distance between two cities is 1887 km. Two trains started from their respective cities at different times. By the time the second train left its city, the first train had already traveled 510 km. The trains met 9 hours after the second train's departure. The speed of the first train is twice the speed of the second train. We need to find the distance between the trains 3 hours after they met.

Solution

Let's break down the problem step by step:

1. Let's assume the speed of the second train is x km/h. Therefore, the speed of the first train is 2x km/h. 2. The first train traveled 510 km by the time the second train started. Let's calculate the time it took for the first train to cover this distance: - Time = Distance / Speed = 510 km / (2x km/h) = 255 / x hours. 3. The trains met 9 hours after the second train's departure. Therefore, the first train traveled for 255 / x hours before the meeting. 4. Now, let's calculate the distance traveled by the first train before the meeting: - Distance = Speed * Time = (2x km/h) * (255 / x) hours = 510 km. - This confirms that the first train traveled 510 km before the meeting. 5. The total distance between the two cities is 1887 km. Therefore, the distance between the trains at the time of the meeting is: - Distance between the trains = Total distance - Distance traveled by the first train = 1887 km - 510 km = 1377 km. 6. After the meeting, the trains continued their journey without stopping. We need to find the distance between the trains 3 hours after the meeting. - Since the first train's speed is 2x km/h, it will cover a distance of 2x km/h * 3 h = 6x km in 3 hours. - Similarly, the second train will cover a distance of x km/h * 3 h = 3x km in 3 hours. - Therefore, the distance between the trains after 3 hours will be 1377 km - (6x km + 3x km) = 1377 km - 9x km.

To find the distance between the trains after 3 hours, we need to determine the value of x.

Calculation

To find the value of x, we can use the information that the trains met 9 hours after the second train's departure. Therefore, the first train traveled for 255 / x hours before the meeting.

Let's set up an equation to solve for x:

255 / x = 9

To solve this equation, we can cross-multiply:

255 = 9x

Dividing both sides by 9:

x = 255 / 9 = 28.33 km/h (approximately)

Now that we have the value of x, we can calculate the distance between the trains after 3 hours:

Distance between the trains after 3 hours = 1377 km - 9x km = 1377 km - 9 * 28.33 km ≈ 1377 km - 255 km ≈ 1122 km.

Answer

The distance between the trains 3 hours after the meeting, if they continued their journey without stopping, is approximately 1122 km.

Please note that the above solution assumes constant speeds for the trains and no other factors affecting their motion.