Question

Помогите решить задачу: От города A до города B поезд шёл 16 часов. Обратный путь этот поезд прошёл со скоростью на 20 километров больше и поэтому прошел весь путь на 4 часа быстрее. С какой скоростью шел поезд от города А до города В и чему равно расстояние?

Answer 1

Пусть Х км/ч скорость от А до В, х+20 км/ч скорость на обратном пути. Расстояние одинаковое, т.к. поезд шел по той же дороге. Зная, что от А до В поезд шел 16 часов, а обратный путь был 16-4 = 12 часов, можно решить уравнение:
16х=(х+20)*12
16х=12х+240
16х-12х=240
4х=240
х=240:4
х=60 км/ч скорость от А до В
60*16=960 км расстояние

Answer 2

Problem Analysis

We are given that a train traveled from city A to city B in 16 hours. On the return journey, the train traveled at a speed 20 kilometers per hour faster and completed the entire journey 4 hours faster. We need to find the speed at which the train traveled from city A to city B and the distance between the two cities.

Solution

Let's assume the speed of the train from city A to city B is x kilometers per hour. Since the train traveled for 16 hours, the distance between the two cities can be calculated using the formula: distance = speed * time.

The distance from city A to city B is 16x kilometers.

On the return journey, the train traveled at a speed 20 kilometers per hour faster, so the speed from city B to city A is x + 20 kilometers per hour. The return journey took 4 hours less, so the time taken for the return journey is 16 - 4 = 12 hours.

Using the same formula, the distance from city B to city A can be calculated as: distance = speed * time. Therefore, the distance from city B to city A is 12(x + 20) kilometers.

Since the distance from city A to city B is the same as the distance from city B to city A, we can set up the following equation:

16x = 12(x + 20)

Solving this equation will give us the value of x, which is the speed of the train from city A to city B.

Calculation

Let's solve the equation:

16x = 12(x + 20)

16x = 12x + 240

4x = 240

x = 60

Therefore, the speed of the train from city A to city B is 60 kilometers per hour.

To find the distance between the two cities, we can substitute the value of x into the formula:

Distance = speed * time

Distance = 60 * 16

Distance = 960 kilometers

Answer

The train traveled from city A to city B at a speed of 60 kilometers per hour and the distance between the two cities is 960 kilometers.