Question

Два поезда вышли в разное время навстречу другу из двух городов, расстояние между которыми 782 км скорость первого поезда 52 км в час, а второго 61 км в час пройдя 416 км, первый поезд встретился со вторым. На сколько один из поездов вышел раньше другого?

Answer 1

416:52=8 часов- двигался первый поезд
782-416=366 км- расстояние, пройденное вторым поездом
366:61= 6 часов-двигался второй поезд
8-6=2 часа
Ответ: первый поезд выехал раньше на 2 часа

Answer 2

Problem Analysis

We are given two trains that start from different cities and travel towards each other. The distance between the cities is 782 km. The first train has a speed of 52 km/h, and the second train has a speed of 61 km/h. We need to determine how much earlier one train left compared to the other.

Solution

To solve this problem, we can use the formula:

Time = Distance / Speed

Let's calculate the time it takes for each train to travel a certain distance and then compare the times to find the time difference.

Let's assume that the first train left x hours earlier than the second train.

The distance traveled by the first train can be calculated using the formula:

Distance = Speed * Time

For the first train: Distance = 52 * (x + Time)

For the second train: Distance = 61 * Time

We know that the distance traveled by the first train is 416 km when the two trains meet. Using this information, we can set up the following equation:

52 * (x + Time) = 416

Simplifying the equation:

52x + 52Time = 416

Now, let's solve for Time:

Time = (416 - 52x) / 52

We can substitute this value of Time into the equation for the distance traveled by the second train:

Distance = 61 * Time

416 = 61 * Time

Simplifying the equation:

Time = 416 / 61

Now, we can calculate the value of x:

x = (416 / 61) - Time

Substituting the value of Time:

x = (416 / 61) - (416 - 52x) / 52

Simplifying the equation:

x = (416 / 61) - (416 / 52) + x

x - x = (416 / 61) - (416 / 52)

Simplifying further:

0 = (416 * 52 - 416 * 61) / (61 * 52 - 52)

x = (416 * 52 - 416 * 61) / (61 * 52 - 52)

Now, let's calculate the value of x:

x = (416 * 52 - 416 * 61) / (61 * 52 - 52) = -0.5

Since the value of x is negative, it means that the second train left 0.5 hours earlier than the first train.

Answer

The second train left 0.5 hours (30 minutes) earlier than the first train.