Question

Из двух городов одновременно навстречу друг другу вышли два поезда Найдите Какая часть пути станет между ними через 1 час 24 минуты если один поезд проходит расстояние между городами за 3 часа 20 минут а второй за 2:48​

Answer 1

Ответ:

2/25

Пошаговое объяснение:

За единицу примем путь (расстояние между городами).

1 ч 24 мин = 1 ч + 24/60 ч = 1 2/5 ч = 7/5 ч - время в пути.

3 ч 20 мин = 3 ч + 20/60 ч = 3 1/3 ч = 10/3 ч - время, за которое 1-й поезд проходит расстояние между городами.

2 ч 48 мин = 2 ч + 48/60 ч = 2 4/5 ч = 14/5 ч - время, за которое 2-й поезд проходит расстояние между городами.

1/(10/3)=3/10 - скорость 1-го поезда.

1/(14/5)=5/14 - скорость 2-го поезда.

3/10 +5/14=21/70 +25/70=46/70=23/35 - скорость сближения.

7/5 ·23/35=23/(5·5)=23/25 - часть пути который поезда проедут.

1 -23/25=25/25 -23/25=2/25 - часть пути, которая останется между ними.

Но для меня было бы обзорно понятнее, если бы я перевёл в десятичную дробь:

23/25=92/100=0,92 - часть пути который поезда проедут.

1-0,92=0,08 - часть пути, которая останется между ними.

Answer 2

Problem Analysis

We have two trains traveling towards each other from two different cities. We are given the time it takes for each train to travel the distance between the cities. We need to find the portion of the distance that will be between the trains after 1 hour and 24 minutes.

Solution

To find the portion of the distance between the trains after 1 hour and 24 minutes, we need to calculate the distance each train has traveled in that time and subtract it from the total distance between the cities.

Let's calculate the distance each train has traveled:

- Train 1: The first train takes 3 hours and 20 minutes (or 200 minutes) to travel the distance between the cities. - Train 2: The second train takes 2 hours and 48 minutes (or 168 minutes) to travel the distance between the cities.

To find the distance each train has traveled in 1 hour and 24 minutes (or 84 minutes), we can use the formula:

Distance = Speed × Time

Let's calculate the distance each train has traveled:

- Train 1: Distance = Speed × Time = (Distance between cities) / (Time taken) × (Time elapsed) = (Distance between cities) / 200 × 84 - Train 2: Distance = Speed × Time = (Distance between cities) / (Time taken) × (Time elapsed) = (Distance between cities) / 168 × 84

To find the portion of the distance between the trains, we subtract the distance traveled by each train from the total distance between the cities:

Portion of distance = Distance between cities - (Distance traveled by Train 1 + Distance traveled by Train 2)

Let's calculate the portion of the distance between the trains:

Portion of distance = (Distance between cities) - [(Distance between cities) / 200 × 84 + (Distance between cities) / 168 × 84]

Now we can substitute the given values and calculate the portion of the distance between the trains.

Calculation

Let's calculate the portion of the distance between the trains using the given values:

- Distance between cities = Unknown (not provided in the question) - Time taken by Train 1 = 3 hours and 20 minutes = 200 minutes - Time taken by Train 2 = 2 hours and 48 minutes = 168 minutes - Time elapsed = 1 hour and 24 minutes = 84 minutes

Portion of distance = (Distance between cities) - [(Distance between cities) / 200 × 84 + (Distance between cities) / 168 × 84]

Since the distance between the cities is not provided in the question, we cannot calculate the exact portion of the distance between the trains without that information.

Please provide the distance between the cities, and I will be able to calculate the portion of the distance between the trains for you.