Question

Из Архангельска вышел пассажирский поезд, который за четверть суток проходит 330 км. Через 1 целую 1\2 ч вслед за ним отправился скорый поезд и через 7 целых 1\2 ч после отправления догнал пассажирский поезд. С какой скоростью шёл скорый поезд?

Answer 1

1)Находим скорость первого (пассажирского) поезда. 330/6= 55 км/ч (где 6 - четвертая часть суток.)
2) Находим сколько времени в  пути был первый поезд (пассажирский) 1,5+7,5=9 часов
3) Находим путь который он (пассажирский поезд) прошел за 9 часов равен: 9*55=495 км
4) Второй поезд (скорый) был в пути 7,5 часов ⇒ его скорость равна 495/7,5=66км/ч

Answer 2

Problem Analysis

We are given that a passenger train from Arkhangelsk travels 330 km in a quarter of a day. After 1 and a half hours, a fast train departs and catches up with the passenger train after 7 and a half hours. We need to determine the speed of the fast train.

Solution

Let's start by calculating the speed of the passenger train.

Given: - Distance traveled by the passenger train = 330 km - Time taken by the passenger train = 1/4 day = 6 hours

To find the speed of the passenger train, we can use the formula:

Speed = Distance / Time

Substituting the given values, we have:

Speed of the passenger train = 330 km / 6 hours

Now, let's calculate the time taken by the fast train to catch up with the passenger train.

Given: - Time taken by the fast train to catch up = 7 and a half hours = 7.5 hours

Since the fast train departs 1 and a half hours after the passenger train, the time taken by the fast train to catch up is the same as the time taken by the passenger train to travel the same distance.

Therefore, the time taken by the fast train to catch up is also 6 hours.

Now, let's calculate the distance traveled by the fast train in 6 hours.

Since the passenger train travels at a constant speed, the distance traveled by the passenger train in 6 hours is the same as the distance traveled by the fast train in 6 hours.

Therefore, the distance traveled by the fast train in 6 hours is 330 km.

Now, we can calculate the speed of the fast train using the formula:

Speed = Distance / Time

Substituting the values, we have:

Speed of the fast train = 330 km / 6 hours

Calculation

Let's calculate the speed of the passenger train and the speed of the fast train.

Speed of the passenger train = 330 km / 6 hours = 55 km/h

Speed of the fast train = 330 km / 6 hours = 55 km/h

Answer

The speed of the fast train is 55 km/h.

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