Question

Алёша сошёл вниз по спускающемуся эскалатору метро за время t1 = 50 с и наступил при этом на N1 = 90 ступенек. Тут же по этой лестнице он пошел вверх и за время подъёма t2 = 150 с наступил на N2 = 135 ступенек. За какое время tx Алёша поднимется по неподвижному эскалатору, если при этом он наступит на N3 = 112 ступенек? Считайте, что Алёша всё время относительно неподвижных платформ метро двигался с постоянной скоростью и наступал на каждую ступеньку.

Answer 1

V+u=90/50 v-u=135/150 v=135/100 t=112/v=112*100/13583 c вроде бы так 

Answer 2

Problem Analysis

In this problem, we are given the time it takes for Aleksey to go down an escalator (t1) and the number of steps he takes (N1). We are also given the time it takes for him to go up the same escalator (t2) and the number of steps he takes (N2). We need to find the time it takes for Aleksey to go up a stationary escalator and the number of steps he takes (N3).

Solution

To solve this problem, we can use the concept of speed. The speed of Aleksey going down the escalator is given by the formula:

Speed = Distance / Time

Since the distance is equal to the number of steps (N1) and the time is equal to t1, we can calculate the speed of Aleksey going down the escalator.

Similarly, the speed of Aleksey going up the escalator is given by the formula:

Speed = Distance / Time

Since the distance is equal to the number of steps (N2) and the time is equal to t2, we can calculate the speed of Aleksey going up the escalator.

Now, to find the time it takes for Aleksey to go up a stationary escalator and the number of steps he takes, we can use the formula:

Time = Distance / Speed

Since the distance is equal to the number of steps (N3) and the speed is equal to the speed of Aleksey going up the escalator, we can calculate the time it takes for Aleksey to go up the stationary escalator.

Let's calculate the values step by step.

Calculation

1. Calculate the speed of Aleksey going down the escalator: - Speed1 = N1 / t1

2. Calculate the speed of Aleksey going up the escalator: - Speed2 = N2 / t2

3. Calculate the time it takes