Question

Поезд шёл из города А в город В, расстояние между которыми 600 км. Когда он прошел 75% всего пути он был задержан на 15 минут, после чего машинист увеличил скорость на 20км/час, и в результате поезд пришёл в город В по расписанию. Чему равна начальная скорость поезда​

Answer 1

Problem Analysis

We are given that a train traveled from city A to city B, a distance of 600 km. When the train had completed 75% of the total distance, it was delayed by 15 minutes. After the delay, the train increased its speed by 20 km/h and arrived in city B on schedule. We need to determine the initial speed of the train.

Solution

Let's assume the initial speed of the train is x km/h.

The train traveled 75% of the total distance, which is 600 km. This means it traveled 75/100 * 600 = 450 km before the delay.

After the delay, the train increased its speed by 20 km/h and completed the remaining 25% of the distance, which is 150 km, on schedule.

To find the initial speed of the train, we can set up the following equation:

Time taken before the delay + Time taken after the delay = Total time

The time taken before the delay can be calculated as distance/speed, and the time taken after the delay can be calculated as distance/(speed + 20).

Substituting the values, we get:

450/x + 150/(x + 20) = Total time

Since the train arrived on schedule, the total time taken before and after the delay should be the same.

Let's solve the equation to find the value of x.

Calculation

450/x + 150/(x + 20) = 450/(x + 20) + 150/(x + 20)

Multiplying through by (x + 20) to eliminate the denominators, we get:

450(x + 20) + 150x = 450 + 150(x + 20)

Expanding and simplifying the equation:

450x + 9000 + 150x = 450 + 150x + 3000

Combining like terms:

600x + 9000 = 450 + 150x + 3000

Subtracting 150x from both sides:

600x + 9000 - 150x = 450 + 150x + 3000 - 150x

450x + 9000 = 450 + 3000

Subtracting 450 from both sides:

450x + 9000 - 450 = 450 + 3000 - 450

450x + 8550 = 3000

Subtracting 8550 from both sides:

450x + 8550 - 8550 = 3000 - 8550

450x = -5550

Dividing by 450:

x = -5550/450

x = -12.33

Since speed cannot be negative, we can conclude that there is an error in the given information or calculations.

Please double-check the problem statement or provide additional information if available.