Question

A man can walk up a moving 'up' escalator in 30 s. The same man can walk down this moving 'up' escalator in 90 s. Assume that his walking speed is the same upwards and downwards. How much time will he take to walk up the escalator, when it is not moving?

• A. 30 s
• B. 45 s
• C. 60 s
• D. 90 s

Hint:

When solving escalator or river-boat problems, always set up equations for relative speed in both directions and solve simultaneously.

Answer 1

The Correct Option is B

Let the length of the escalator be $L$, the man's walking speed be $m$, and the escalator's speed be $e$. Upwards on moving escalator: \[ \frac{L}{m + e} = 30 \quad \Rightarrow \quad L = 30(m + e) \] Downwards on moving 'up' escalator: \[ \frac{L}{m - e} = 90 \quad \Rightarrow \quad L = 90(m - e) \] Equating both expressions for $L$: \[ 30(m + e) = 90(m - e) \] \[ m + e = 3m - 3e \] \[ 2m = 4e \quad \Rightarrow \quad m = 2e \] Substitute $m = 2e$ into $L = 30(m + e)$: \[ L = 30(2e + e) = 90e \] When escalator is stationary: \[ \frac{L}{m} = \frac{90e}{2e} = 45 \ \text{s} \] Thus, time taken is 45 s.