Question

ПОМОГИТЕ ПОЖАЛУЙСТА, НИКАК НЕ МОГУ РЕШИИТЬ( 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

По моим расчетам (долго писать их :)), $t _{x} =100 c$

Answer 2

Problem Analysis

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

Solution

To solve this problem, we can use the concept of speed. The speed of Alesha while going down the escalator is given by N1/t1, and the speed while going up is given by N2/t2. Since the escalator is stationary, the speed of Alesha while going up the stationary escalator will be the same as his speed while going up the moving escalator.

We can use the formula speed = distance/time to find the time it will take Alesha to go up the stationary escalator. The distance he needs to cover is N3, and the speed is N2/t2. Therefore, the time it will take him to go up the stationary escalator (tx) can be calculated as:

tx = N3 / (N2 / t2)

Let's substitute the given values into the formula to find the value of tx.

Given: - N1 = 90 steps - t1 = 50 seconds - N2 = 135 steps - t2 = 150 seconds - N3 = 112 steps

Substituting the values into the formula:

tx = 112 / (135 / 150)

Calculating the value of tx:

tx = 112 / (0.9)

tx = 124.44 seconds

Therefore, it will take Alesha approximately 124.44 seconds to go up the stationary escalator and he will take 112 steps.

Answer

Alesha will take approximately 124.44 seconds to go up the stationary escalator, and he will take 112 steps.