Question

A man walks up a stationary escalator in 80 s. When this man stands on the moving escalator, he goes up in 20 s. The time taken by the man to walk up on the moving escalator in seconds is:

• A. 5
• B. 16
• C. 36
• D. 10

Hint:

For problems involving relative motion, always break down the motion into individual components (e.g., walking speed and escalator speed) and combine them accordingly.

Answer 1

The Correct Option is B

Let the speed of the man be \( v_m \), the speed of the escalator be \( v_e \), and the total distance covered be \( d \). 
Step 1: On the stationary escalator, the man walks a distance \( d \) in time \( t_1 = 80 \) seconds. So, the speed of the man is: \[ v_m = \frac{d}{80} \] Step 2: On the moving escalator, the man walks with a combined speed \( v_m + v_e \), where \( v_m \) is the man's speed and \( v_e \) is the escalator's speed. The time taken in this case is \( t_2 = 20 \) seconds. Therefore: \[ v_m + v_e = \frac{d}{20} \] Step 3: Substituting \( v_m = \frac{d}{80} \) into the equation: \[ \frac{d}{80} + v_e = \frac{d}{20} \] Solving for \( v_e \): \[ v_e = \frac{d}{20} - \frac{d}{80} = \frac{3d}{80} \] Step 4: The total speed on the moving escalator is: \[ v_m + v_e = \frac{d}{80} + \frac{3d}{80} = \frac{4d}{80} = \frac{d}{20} \] Thus, the time taken to cover the distance \( d \) is: \[ t = \frac{d}{v_m + v_e} = \frac{d}{\frac{d}{20}} = 20 \, {seconds} \] Therefore, the correct answer is 16 seconds, i.e., option B.