Question

Скорый поезд проходит расстояние от Москвы до Петербурга за 12ч, а экспресс за 10 ч.Через 0,75 ч после выхода Скорого поезда тоже вышел экспресс.Через сколько часов после своего выхода он догонит скорый поезд?

Answer 1

Это действительно сложная задача

Answer 2

Problem Analysis

We are given that a fast train travels from Moscow to St. Petersburg in 12 hours, while an express train takes 10 hours. We are also told that the express train departs 0.75 hours after the fast train. We need to determine how many hours after its departure the express train will catch up to the fast train.

Solution

To solve this problem, we can calculate the relative speed between the two trains and use it to determine the time it takes for the express train to catch up to the fast train.

Let's assume that the distance between Moscow and St. Petersburg is D kilometers.

The fast train takes 12 hours to cover this distance, so its speed can be calculated as D / 12 kilometers per hour.

The express train takes 10 hours to cover the same distance, so its speed can be calculated as D / 10 kilometers per hour.

Since the express train departs 0.75 hours after the fast train, it has been traveling for 0.75 hours less than the fast train when we start comparing their positions.

Let's denote the time it takes for the express train to catch up to the fast train as t hours.

During this time, the fast train will have traveled (D / 12) * t kilometers, and the express train will have traveled (D / 10) * (t - 0.75) kilometers.

To find the time when the express train catches up to the fast train, we need to set these two distances equal to each other and solve for t:

(D / 12) * t = (D / 10) * (t - 0.75)

Simplifying the equation:

(D / 12) * t = (D / 10) * t - (D / 10) * 0.75

Multiplying both sides by 12 (to eliminate the denominators):

10 * D * t = 12 * D * t - 9 * D

Simplifying further:

10 * D * t - 12 * D * t = -9 * D

-2 * D * t = -9 * D

Dividing both sides by -2D:

t = 9 / 2 = 4.5 hours

Therefore, the express train will catch up to the fast train 4.5 hours after its own departure.

Answer

The express train will catch up to the fast train 4.5 hours after its own departure.