Question

Грузовой поезд проехал 420 км, сделав остановку на одной станции. Путь до этой станции занял 4 часа при скорости 80км/час. Весь оставшийся путь занял 2 часа. С какой скоростью поезд двигался после остановки? ____ нужно решить 2-мя способами арифметическим и алгебраическим

Answer 1

1) 80·4=320 (км) - проехал поезд до остановки
2) 420-320=100 (км) - после остановки
3) 100:2=50 (км/ч) - скорость после остановки
Ответ: 50 км/ч.
Что такое алгебраический способ для этой задачи - я, честно, признаюсь, не понимаю. За х здесь обозначить нечего.
Единственное, что можно сделать - это составить выражение:
(420-80·4):2=50 (км/ч)

Пусть скорость после остановки равна х км/ч, тогда за 2 ч поезд проехал 2х км/ч. До остановки он проехал за 4 ч сос коростью 80 км/ч 4·80 км. Т. к. всего он проехал 420 км, то составим и решим уравнение
4·80+2х=420,
320+2х=420,
2х=420-320,
2х=100, х=100:2,
х=50.

Answer 2

Problem Statement

A freight train traveled a distance of 420 km, making a stop at one station. The journey to this station took 4 hours at a speed of 80 km/h. The remaining distance took 2 hours. What was the speed of the train after the stop? Solve the problem using both arithmetic and algebraic methods.

Arithmetic Solution

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

Speed = Distance / Time

Let's calculate the distance traveled before the stop:

Distance before the stop = Speed * Time = 80 km/h * 4 hours = 320 km

Now, we can calculate the distance traveled after the stop:

Distance after the stop = Total distance - Distance before the stop = 420 km - 320 km = 100 km

The time taken to travel the remaining distance is given as 2 hours.

Now, we can calculate the speed of the train after the stop:

Speed after the stop = Distance after the stop / Time = 100 km / 2 hours = 50 km/h

Therefore, the speed of the train after the stop is 50 km/h.

Algebraic Solution

Let's assume the speed of the train after the stop as 'x' km/h.

The distance traveled before the stop is given as 320 km, and the time taken is 4 hours. Therefore, we can write the equation:

320 km = 80 km/h * 4 hours

Simplifying the equation, we get:

320 km = 320 km

This equation is true, which means the distance traveled before the stop is correct.

Now, let's calculate the distance traveled after the stop:

Distance after the stop = Total distance - Distance before the stop = 420 km - 320 km = 100 km

The time taken to travel the remaining distance is given as 2 hours. Therefore, we can write the equation:

100 km = x km/h * 2 hours

Simplifying the equation, we get:

100 km = 2x km/h

Dividing both sides of the equation by 2, we get:

50 km = x km/h

Therefore, the speed of the train after the stop is 50 km/h.

Both the arithmetic and algebraic methods yield the same result, which is 50 km/h.