Question

Из двух городов, между которыми равно 1200км пути, одновременно навстречу друг другу выехали два поезда. Один из них затрачивает на этот путь 20 ч, другой-30 ч. Через сколько часов встретятся поезда

Answer 1

1) 1200 км : 20 часов = 60 км/час - скорость первого поезда

2) 1200 км : 30 ч = 40 км/час - скорость второго

3) 60 км/час + 40 км/час = 100 км/час - скорость сближения поездов

4) 1200км : 100 км/час = 12 часов

Ответ: Поезда встретятся через 12 часов

Answer 2

Problem Analysis

We are given that two trains start simultaneously from two cities that are 1200 km apart. One train takes 20 hours to cover the distance, while the other train takes 30 hours. We need to determine how many hours it will take for the trains to meet.

Solution

To solve this problem, we can use the concept of relative speed. The relative speed between two objects moving towards each other is the sum of their individual speeds. In this case, the relative speed of the two trains is the sum of their speeds.

Let's assume the speed of the first train is v1 and the speed of the second train is v2. We are given that the distance between the two cities is 1200 km. We can use the formula:

Time = Distance / Speed

To find the time it takes for the trains to meet, we need to divide the distance between the two cities by the sum of their speeds.

Let's calculate the time it takes for the trains to meet:

Time = 1200 km / (v1 + v2)

Now, let's substitute the given values into the formula:

Time = 1200 km / (v1 + v2)

We are not given the speeds of the trains directly, but we are given the time it takes for each train to cover the distance. We can use the formula:

Speed = Distance / Time

Let's calculate the speeds of the trains:

Speed of the first train (v1) = 1200 km / 20 hours

Speed of the second train (v2) = 1200 km / 30 hours

Now, let's substitute the calculated speeds into the formula for time:

Time = 1200 km / ((1200 km / 20 hours) + (1200 km / 30 hours))

Simplifying the equation:

Time = 1200 km / (60 km/h + 40 km/h)

Time = 1200 km / 100 km/h

Time = 12 hours

Therefore, the two trains will meet after 12 hours.

Answer

The two trains will meet after 12 hours.

Explanation

The time it takes for the two trains to meet can be calculated using the formula: Time = Distance / (Speed of train 1 + Speed of train 2). In this case, the distance between the two cities is 1200 km, and the speeds of the trains are calculated to be 60 km/h and 40 km/h. Substituting these values into the formula, we find that the two trains will meet after 12 hours.