JEE Main · 2021 · 20 Jul 2021 · Shift 2 · Kinematics

A boy reaches the airport and finds that the escalator is not working. He walks up the stationary escalator in time

t_{1}

. If he remains stationary on a moving escalator then the escalator takes him up in time

t_{2}

. The time taken by him to walk up on the moving escalator will be :

Answer: (A)

Solution

Let the escalator have length

L

. Walking up it while it is stationary shows that the boy moves at

\frac{L}{t _{1}}

, and standing on it while it runs shows that the escalator moves at

\frac{L}{t _{2}}

. When he walks up the moving escalator the two speeds add, so the time taken is

t = \frac{L}{\frac{L}{t _{1}} + \frac{L}{t _{2}}} = \frac{t _{1} t _{2}}{t _{1} + t _{2}}

He reaches the top in a time

\frac{t _{1} t _{2}}{t _{2} + t _{1}}

JEE Main · 2021 · 20 Jul 2021 · Shift 2 · Single correct option