Calculating the number of steps in an escalator

[viren_t2005]

There is a escalator and 12 persons move down it. A takes 50 steps and B takes 75 steps while the escalator is moving down.Given that the time taken by A to take 1 step is equal to time taken by B to take 3 steps. Find the no.of steps in the escalator while it is stationary

 

[vaishakh]

I think I am correct. Let x be the number of steps covered by A in the given time and let y be the steps escalator sailed. then
x + y = 50
3x + y = 75.
Thus we will get the answer y as to be 37.5

 

[Architeuthis Dux]

To calculate the number of steps in an escalator, we first need to determine the time it takes for each person to take one step. From the given information, we know that A takes 50 steps and B takes 75 steps while the escalator is moving down. We are also given that A takes the same amount of time to take one step as B takes to take three steps.

Based on this information, we can set up the following equation:

50 steps / (time taken by A to take 1 step) = 75 steps / (time taken by B to take 3 steps)

Simplifying this equation, we get:

50 / x = 75 / (3x)

Where x represents the time taken for A to take one step.

Solving for x, we get x = 2.5.

This means that A takes 2.5 seconds to take one step while B takes 7.5 seconds to take three steps.

Now, if we assume that the escalator is stationary, the time taken by A and B to take one step will be the same. Therefore, we can set up another equation:

50 steps / (time taken by A to take 1 step) = 75 steps / (time taken by B to take 1 step)

Substituting x = 2.5 in this equation, we get:

50 / 2.5 = 75 / y

Where y represents the time taken for B to take one step.

Solving for y, we get y = 3.33.

This means that B takes 3.33 seconds to take one step while the escalator is stationary.

Now, to calculate the number of steps in the escalator, we can use the formula:

(Number of steps taken by A) * (Time taken by A to take one step) = (Number of steps taken by B) * (Time taken by B to take one step)

Substituting the values, we get:

50 * 2.5 = (Number of steps) * 3.33

Solving for the number of steps, we get:

Number of steps = 125 / 3.33 = 37.5

Therefore, the number of steps in the escalator while it is stationary is approximately 37.5. However, this is an approximation and the exact number may vary slightly