Question

a man walk up a stationry escalator in 90 sec when this man stands on a moving escalator he goes up in 60sec the time taken by the man to walk up the moving escalator is ?

Answer 1

Answer on Question #47242 – Physics - Mechanics | Kinematics | Dynamics

a man walk up a stationary escalator in 90 sec when this man stands on a moving escalator he goes up in 60 sec the time taken by the man to walk up the moving escalator is ?

Solution:

Let the distance of the escalator be $S$;

$u$ – velocity of the escalator;

$v$ – velocity of the man;

$t_1 = 90\, s$ – time to walk up stationary escalator;

$t_2 = 60\, s$ – time to stand on a moving escalator;

$t_3$ – time to go up on a moving escalator;

On a stationary escalator:

$$t_1 = \frac{S}{v}$$ $$v = \frac{S}{t_1} \quad (1)$$

On a moving escalator:

$$t_2 = \frac{S}{u}$$ $$u = \frac{S}{t_2} \quad (2)$$

Walking up on a moving escalator:

$$t_3 = \frac{S}{u + v} \quad (3)$$

(1) and (2) in (3):

$$t_3 = \frac{S}{\frac{S}{t_1} + \frac{S}{t_2}} = \frac{S}{\frac{S(t_1 + t_2)}{t_1 t_2}} = \frac{t_1 t_2}{t_1 + t_2} = \frac{90\, s \cdot 60\, s}{90\, s + 60\, s} = 36\, s$$

Answer: 36 sec

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