Question

It takes one minute for a passenger standing on an escalator to reach the top. If the escalator does not move it takes him $3$ minute to walk up. How long will it take for the passenger to arrive at the top if he walks up the moving escalator?

• A. 30 s
• B. 45 s
• C. 40 s
• D. 35 s

Answer 1

Answer: (B)

Let speed of elevator be $v_e$.
$t_1 = \frac{L}{v_{e}}$
$\Rightarrow 1\, \min = \frac{L}{v_{e}}$
Let speed of person relative to elevator be $v_P$, then
$t_2 = \frac{L}{v_{p}}$
$\Rightarrow 3\, \min = \frac{L}{v_{p}}$
when the escalator is moving:
$t_3 = \frac{L}{v_{e} + v_{p}} $
$= \frac{L}{\frac{L}{1\, \min} + \frac{L}{3\, \min}}$
$=\frac{3}{4} \min = 45\,s$