Relative Motion

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 be the length of the escalator.
Let be the speed of the person walking on the escalator (in units of ).
Let be the speed of the escalator (in units of ).
Step 2: Analyze the given information
1. Walking up the stalled escalator:
The escalator is not moving, so the person's speed is .
The time taken to walk up the stalled escalator is 90 seconds.
Thus: 2. Standing on the moving escalator:
The person is not walking, so the escalator's speed is .
The time taken to reach the top is 60 seconds. Thus:
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: Substitute the values of and : To add these fractions, find a common denominator (180): Step 4: Calculate the time to walk up the moving escalator The time to walk up the moving escalator is given by: Substitute : Final Answer: The time it would take the person to walk up the moving escalator is: