Question

Ускоренный поезд проходит расстояние от Москвы до Ленинграда за 12 часов, а скорый - за 10 часов. Через 3/4 часа после выхода из Москвы ускоренного поезда выходит из Москвы скорый. Через сколько часов скорый поезд догонит ускоренный?

Answer 1

Ускоренный поезд доедет через 10 часов

Answer 2

Problem Analysis

We are given that an express train travels from Moscow to Leningrad in 12 hours, while a fast train takes 10 hours. The fast train departs from Moscow 3/4 of an hour after the express train. We need to determine how many hours it will take for the fast train to catch up to the express train.

Solution

Let's assume that the express train's speed is x km/h and the fast train's speed is y km/h.

We can use the formula distance = speed × time to calculate the distance traveled by each train.

For the express train: - Speed: x km/h - Time: 12 hours - Distance: x × 12 km

For the fast train: - Speed: y km/h - Time: 10 hours - Distance: y × 10 km

Since the fast train departs from Moscow 3/4 of an hour after the express train, it will have been traveling for 3/4 of an hour less than the express train when it starts to catch up.

Let's calculate the distance traveled by the fast train when it starts to catch up to the express train.

The time it takes for the fast train to catch up to the express train is the same as the time it takes for the fast train to cover the distance traveled by the express train minus the distance traveled by the fast train.

So, the time it takes for the fast train to catch up is:

12 - (10 - 3/4) = 12 - 9 1/4 = 2 3/4 hours

Therefore, the fast train will catch up to the express train in 2 hours and 45 minutes.

Answer

The fast train will catch up to the express train in 2 hours and 45 minutes.

Note: The answer provided is based on the information given in the problem statement and the calculations made.