Question

A person walks up a stalled escalator in 90s. When standing on the same moving escalator, he reached in 60s. The time it would take him to walk up the moving escalator will be:

• A. 36 s
• B. 72 s
• C. 18 s
• D. 27 s

Hint:

When dealing with motion problems involving combined speeds, use the relationship between distance, speed, and time to set up equations and solve for the unknown.

Answer 1

The Correct Option is A

To solve this problem, we need to determine the time it would take for the person to walk up the moving escalator. We will analyze the situation using relative speeds. Step 1: Define the variables
Let \( L \) be the length of the escalator.
Let \( v_p \) be the speed of the person walking on the escalator (in units of \( L/s \)).
Let \( v_e \) be the speed of the escalator (in units of \( L/s \)).
Step 2: Analyze the given information
1. Walking up the stalled escalator:
The escalator is not moving, so the person's speed is \( v_p \).
The time taken to walk up the stalled escalator is 90 seconds.
Thus: \[ v_p = \frac{L}{90}. \] 2. Standing on the moving escalator:
The person is not walking, so the escalator's speed is \( v_e \).
The time taken to reach the top is 60 seconds. Thus:
\[ v_e = \frac{L}{60}. \] Step 3: Determine the combined speed When the person walks up the moving escalator, their effective speed is the sum of their walking speed and the escalator's speed: \[ v_{\text{combined}} = v_p + v_e. \] Substitute the values of \( v_p \) and \( v_e \): \[ v_{\text{combined}} = \frac{L}{90} + \frac{L}{60}. \] To add these fractions, find a common denominator (180): \[ v_{\text{combined}} = \frac{2L}{180} + \frac{3L}{180} = \frac{5L}{180} = \frac{L}{36}. \] Step 4: Calculate the time to walk up the moving escalator The time \( t \) to walk up the moving escalator is given by: \[ t = \frac{L}{v_{\text{combined}}}. \] Substitute \( v_{\text{combined}} = \frac{L}{36} \): \[ t = \frac{L}{\frac{L}{36}} = 36 \, \text{seconds}. \] Final Answer: The time it would take the person to walk up the moving escalator is: \[ \boxed{36 \, \text{s}} \]