Question

A person walks up a stationary escalator in time $t_1$. If he remains stationary on the escalator, then it can take him up in time $t_2$. How much time would it take him to walk up the moving escalator?

• A. $\frac{t_1+t_2}{2}$
• B. $\sqrt{t_1{t}_2}$
• C. $\frac{t_1{t}_2}{t_1+t_2}$
• D. $t_1+t_2$

Answer 1

Answer: (C)

Let $L$ be the length of escalator.
Speed of man w.r.t. escalator is $v_{mc}=\frac{L}{t_1}$
Speed of escalator is $v_c=\frac{L}{t_2}$
$\therefore$ Speed of man with respect to ground would be
$v_m=v_{mc}+v_c=L\left(\frac{1}{t_1}+\frac{1}{t_2}\right)$
$\therefore$ Time taken $t=\frac{L}{L\left(\frac{1}{t_1}+\frac{1}{t_2}\right)}=\frac{t_1{t}_2}{t_1+t_2}$