When a man stands m a moving escalted the goes up in 50 sec and when he walks up the moving escalator he goes in 30 sec,then find the five in which man walks up the stationar escalator.

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Solution

Escalator speed, $u$

Man walking speed, $v$

Total distance, $s$

Time (escalator moving, man stationary), $t_{1} = 50 sec = \frac{s}{u} . . . . . (1)$

Time (escalator and man both moving), $t_{2} = 30 sec = \frac{s}{u + v} . . . (2)$

Time (escalator stationary, man moving) $t_{3} = \frac{s}{v} . . . . . (3)$

From (1), (2) and (3).

$\frac{1}{t_{2}} = \frac{1}{t_{1}} + \frac{1}{t_{3}}$

$\Rightarrow \frac{1}{30} = \frac{1}{50} + \frac{1}{t_{3}}$

$\Rightarrow t_{3} = 75 sec$

Hence, time taken by man to reach is $75 sec$

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