A person walks up a stalled 15 m long escalator in 90 s. When standing on the same escalator, now moving, the person is carried up in 60 s. How much time would it take that person to walk up the moving escalator? Does the answer depend on the length of the escalator?

Explanation

To solve the problem, we need to determine how long it would take for a person to walk up a moving escalator, given the time it takes for them to walk up a stationary escalator and the time it takes for them to be carried up by the moving escalator.

### Step-by-Step Solution:

1. **Identify the Variables:**
- Let \( L \) be the length of the escalator, which is given as 15 m.
- Let \( t_1 = 90 \) s be the time taken for the person to walk up the stationary escalator.
- Let \( t_2 = 60 \) s be the time taken for the person to be carried up the moving escalator.

2. **Calculate the Speeds:**
- The speed of the person walking (\( v_1 \)) can be calculated using the formula:
\[ v_1 = \frac{L}{t_1} = \frac{15 \, \text{m}}{90 \, \text{s}} = \frac{1}{6} \, \text{m/s} \]
- The speed of the escalator (\( v_2 \)) can be calculated as:
\[ v_2 = \frac{L}{t_2} = \frac{15 \, \text{m}}{60 \, \text{s}} = \frac{1}{4} \, \text{m/s} \]

3. **Determine the Time to Walk Up the Moving Escalator:**
- When the person is walking up the moving escalator, their effective speed is the sum of their walking speed and the escalator's speed:
\[ v_{\text{effective}} = v_1 + v_2 = \frac{1}{6} + \frac{1}{4} \]
- To add these fractions, find a common denominator (which is 12):
\[ v_{\text{effective}} = \frac{2}{12} + \frac{3}{12} = \frac{5}{12} \, \text{m/s} \]

4. **Calculate the Time Taken to Walk Up the Moving Escalator:**
- The time taken (\( t \)) to walk up the moving escalator can be calculated using:
\[ t = \frac{L}{v_{\text{effective}}} = \frac{15 \, \text{m}}{\frac{5}{12} \, \text{m/s}} = 15 \times \frac{12}{5} = 36 \, \text{s} \]

5. **Conclusion:**
- The time taken for the person to walk up the moving escalator is **36 seconds**.
- The answer does not depend on the length of the escalator because the relationship between the speeds and times remains consistent regardless of the length.