Question

Скорый поезд проезжает мимо столба за 9 сек , а мимо перрона длиной 336 м за 23 сек . Какова длина поезда , если его скорость постоянна ?

Answer 1

Поезд проезжает мимо столба х м (т.е расстояние, равное длине поезда) за 9 сек, т.е скорость=х/9 м/сек
мимо перрона (х+336)м (т.е длинна поезда+длинна перрона) за 23 сек
скорость равна (х+336)/23 м/сек
(х+336)/23=х/9
9х+9*336=23х
14х=3024
х=216 м
ответ длина поезда 216м

Answer 2

Problem Analysis

We are given that a fast train passes by a pole in 9 seconds and passes by a platform with a length of 336 meters in 23 seconds. We need to find the length of the train assuming its speed is constant.

Solution

Let's assume the length of the train is L meters and its speed is S meters per second.

When the train passes by the pole, it covers a distance equal to its own length in 9 seconds. Therefore, we can write the equation:

L = S * 9 Similarly, when the train passes by the platform, it covers a distance equal to the sum of its own length and the length of the platform (336 meters) in 23 seconds. Therefore, we can write the equation:

L + 336 = S * 23 We have a system of two equations with two unknowns (L and S). We can solve this system of equations to find the length of the train.

To solve the system, we can rearrange equation to express S in terms of L:

S = L / 9 Substituting equation into equation we get:

L + 336 = (L / 9) * 23

Simplifying the equation:

9L + 3024 = 23L

14L = 3024

L = 216

Therefore, the length of the train is 216 meters.

Answer

The length of the train is 216 meters.

Verification

Let's verify the answer using the given information.

According to the problem statement, the train passes by the pole in 9 seconds. If we substitute the length of the train (216 meters) and the time (9 seconds) into equation we get:

216 = S * 9

Simplifying the equation:

S = 216 / 9

S = 24

So, the speed of the train is 24 meters per second.

Now, let's check if the train passes by the platform with a length of 336 meters in 23 seconds. If we substitute the length of the train (216 meters), the length of the platform (336 meters), and the speed (24 meters per second) into equation we get:

216 + 336 = 24 * 23

Simplifying the equation:

552 = 552

The equation is true, which means our answer is correct.

Therefore, the length of the train is 216 meters.