Question

Школьник владислав идет по движущемуся вверх эскалатору, поднимаясь за 20 с. Школьник Ярослав, стоя на том же эскалаторе, поднимается за 60 с. За какое время Владислав будет подниматься по эскалатору вверх, если эскалатор запустить в обратном направлении с такой же по модулю скоростью, как и при движении наверх? Даю 30 баллов!!!

Answer 1

60-20=40с-за такое время влад поднимется по эскалатару, идущему вниз

Answer 2

Problem Analysis

We are given that Vladislav takes 20 seconds to go up an escalator, while Yaroslav takes 60 seconds to go up the same escalator. We need to find out how long Vladislav will take to go up the escalator if it is running in the opposite direction at the same speed.

Solution

Let's assume the speed of the escalator is x units per second. Since Vladislav takes 20 seconds to go up the escalator, his effective speed (relative to the ground) is 1 unit per second (since he covers the entire distance in 20 seconds). Similarly, Yaroslav's effective speed is 1/3 units per second (since he covers the entire distance in 60 seconds).

When the escalator is running in the opposite direction, Vladislav's effective speed will be the difference between his speed and the speed of the escalator. So, his effective speed will be (1 - x) units per second.

To find the time it takes for Vladislav to go up the escalator when it is running in the opposite direction, we can use the formula:

Time = Distance / Speed

Since the distance is the same for both Vladislav and Yaroslav, we can set up the equation:

20 = Distance / (1 - x)

Simplifying the equation, we get:

Distance = 20 * (1 - x)

Similarly, for Yaroslav, we can set up the equation:

60 = Distance / (1/3)

Simplifying the equation, we get:

Distance = 60 * (1/3)

Since the distances are equal, we can equate the two expressions for distance:

20 * (1 - x) = 60 * (1/3)

Simplifying the equation, we get:

1 - x = 1/9

Solving for x, we get:

x = 8/9

Therefore, when the escalator is running in the opposite direction at a speed of 8/9 units per second, Vladislav will take 20 seconds to go up the escalator.

Answer

Vladislav will take 20 seconds to go up the escalator when it is running in the opposite direction at a speed of 8/9 units per second.