A person walks up a stationary escalation in $t_{1}$ second. If he remains stationary on the escalator, then it can take him up in $t_{2}$ second. If the length of the escalator is L, then
a. Determine the speed of man with respect to the escalator.
b. Determine the speed of the escalator.
c. How much time would it take him to walk up the moving escalator?

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Solution

a. As the escalator is stationary, so the distance covered in $t_{1}$ seconds is L which is the length of the escalator.
Speed of man w.r.t. the escalator, $v_{m e} = \frac{L}{t_{1}}$

b.When the man is stationary, by taking man as a reference point the distance covered by escalator is L in time $t_{2}$ .
Speed of escalator, $v_{c} = \frac{L}{t_{2}}$

c. Speed of man w.r.t. the ground, $v_{m} = v_{m e} + v_{c}$ _
$\Rightarrow v_{m} = \frac{L}{t_{1}} + \frac{L}{t_{2}}$ = $L [\frac{1}{t_{1}} + \frac{1}{t_{1}}]$ = $L [\frac{t_{1} + t_{2}}{t_{1} t_{2}}]$
$∴ t = \frac{L}{v_{m}} = [\frac{t_{1} t_{2}}{t_{1} + t_{2}}]$
which is the time taken by the man to walk up the moving escalator.

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