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  • At a metro station, a girl walks up a stationary escalator in time t_{1}. If she remains stationary on the escalator, then the escalator take her up in time t_{2}. The time taken by her to walk up on the moving escalator will be

At a metro station, a girl walks up a stationary escalator in time t1. If she remains stationary on the escalator, then the escalator take her up in time t_{2}. The time taken by her to walk up on the moving escalator will be

a) \frac{(t_{1}+t_{2})}{2}

b) \frac{t_{1}t_{2}}{(t_{2}-t_{1})}

c) \frac{t_{1}t_{2}}{(t_{2}+t_{1})}

d) \; t_{1}-t_{2}

Answers (1)

The answer is the option c) \frac{t_{1}t_{2}}{(t_{2}+t_{1})}

Explanation: Let us consider L as the length of the escalator,

V_{g} as the velocity of the girl w.r.t. the ground

& V_{e} as the velocity of the escalator w.r.t. the ground

Now, w.r.t. the ground, the effective velocity of the girl will be,

V_{g}+V_{e}=\frac{L}{t_{1}} + \frac{L}{t_{2}}

                  =L(\frac{1}{t_{1}} + \frac{1}{t_{2}})

V_{ge}=L\left [ \frac{t_{1}+t_{2}}{t_{1}t_{2}} \right ]

\\\frac{L}{t}=L[\frac{t_1+t_2}{t_1t_2}]\\t=\frac{t_1 t_2}{t_1+t_2}

 

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infoexpert22

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