Question

A person walked up a stalled escalator in $90\, s$ . When standing on the same escalator, now moving, he is carried up in $60\, s$. How much time would it take him to walk up the moving escalator?

• A. 36s
• B. 30s
• C. 60s
• D. 26s

Answer 1

The Correct Option is A

To solve this problem, we need to use the concept of relative speed in physics. The situation here includes a person walking on a stalled escalator and then being carried by the moving escalator. We need to determine the time it will take for the person to walk on the moving escalator.

1. Let's denote the length of the escalator as L.
2. When the escalator is stalled, the person takes 90\, \text{s} to walk up, so the person's walking speed is:
   v_{\text{person}} = \frac{L}{90}\, \text{m/s}
3. When the person is standing on the moving escalator, it takes 60\, \text{s} to travel the entire length, so the speed of the escalator is:
   v_{\text{escalator}} = \frac{L}{60}\, \text{m/s}
4. When the person walks on the moving escalator, the effective speed is the sum of the person's walking speed and the escalator's speed:
   v_{\text{effective}} = v_{\text{person}} + v_{\text{escalator}}
   v_{\text{effective}} = \frac{L}{90} + \frac{L}{60}
   To combine these, find a common denominator:
   v_{\text{effective}} = \frac{2L}{180} + \frac{3L}{180} = \frac{5L}{180} = \frac{L}{36}\, \text{m/s}
5. The time taken to walk up the moving escalator is:
   t_{\text{effective}} = \frac{L}{v_{\text{effective}}} = \frac{L}{\frac{L}{36}} = 36\, \text{s}

Therefore, the time it takes for the person to walk up the moving escalator is 36 seconds, which is the correct option.