Question

A boy takes $90$ second to walk up a stalled escalator. However, if the escalator is moving and he stands on the escalator, he is carried up in one minute. how much time the boy would take to walk up the moving escalator?

• A. $36\text{s}$
• B. $40\text{s}$
• C. $41.25\text{s}$
• D. $43.75\text{s}$

Answer 1

The correct option is A $36\text{s}$

Let $v_b$ be the velocity of the boy relative to the escalator and $v_e$ be the velocity of the escalator. Then, the relative velocity of the boy with respect to the ground in the moving escalator is $(v_b+v_e)$.
If $l$ is the length of the escalator, then
$\frac{l}{v_b}=90,\frac{l}{v_e}=60,\frac{l}{v_b+v_e}=t$

$\frac{1}{t}=\frac{v_b+v_e}{l}=\frac{v_b}{l}+\frac{v_e}{l}=\frac{1}{90}+\frac{1}{60}$

$\frac{1}{t}=\frac{60+90}{90\times 60}=\frac{150}{90\times 60}=\frac{1}{36}$

$t=36\text{s}$