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 $3$ minutes to walk up. How long will it take for the passenger to arrive at the top if he walks up the moving escalator?

• A. $25sec$
• B. $30sec$
• C. $35sec$
• D. $45sec$

Answer 1

The correct option is D $45sec$

Let the length of elevator be $L$
Let speed of elevator be $v_e$
$t_1=\frac{L}{v_e}$
$1min=\frac{L}{v_e}$

Let speed of person on still escalator is $v_p$, then
$t_2=\frac{L}{v_p}$
$3min=\frac{L}{v_p}$

when the escalator is moving:
$t_3=\frac{L}{v_e+v_p}$

$t_3=\frac{L}{\frac{L}{1min}+\frac{L}{3min}}=\frac{3}{4}min$

$t_3=45sec$

Final Answer: (b)