Question

Решите задачу составив числовое выражение: Расстояние между двумя станциями железной дороги равно 900 км. С этих станций навстречу друг другу вышли одновременно два поезда.Один из них шел со скоростью 40 километров в час, а другой 35 километров в час. Через сколько часов они встретятся?

Answer 1

900:(40+35) = 900:75 = 12 (ч) поезда встретятся.
Ответ: через 12 часов они встретятся.

Answer 2

Problem Analysis

We are given that the distance between two railway stations is 900 km. Two trains start from these stations simultaneously, with one train traveling at a speed of 40 km/h and the other at 35 km/h. We need to determine how many hours it will take for the trains to meet.

Solution

To solve this problem, we can use the formula: time = distance / speed.

Let's assume that the time it takes for the trains to meet is t hours.

The distance traveled by the first train in t hours is 40t km, and the distance traveled by the second train in t hours is 35t km.

Since the total distance between the two stations is 900 km, the sum of the distances traveled by the two trains should be equal to 900 km:

40t + 35t = 900

Simplifying the equation:

75t = 900

Dividing both sides of the equation by 75:

t = 900 / 75 = 12

Therefore, it will take 12 hours for the two trains to meet.

Answer

The two trains will meet after 12 hours.

Verification

Let's verify the answer using the given information.

The first train travels at a speed of 40 km/h, so in 12 hours, it will cover a distance of 40 * 12 = 480 km.

The second train travels at a speed of 35 km/h, so in 12 hours, it will cover a distance of 35 * 12 = 420 km.

The sum of the distances covered by the two trains is 480 + 420 = 900 km, which matches the total distance between the two stations.

Therefore, the answer is verified.