Question

A man walks up a stationary escalator in $90\,\,s$. When this man stands on a moving escalator, he goes up in $60\,\,s$. The time taken by the man to walk up the moving escalator is
(A) $30\,\,s$
(B) $45\,\,s$
(C) $36\,\,s$
(D) $48\,\,s$

Answer 1

Hint
The above given problem can be solved using the formula derived for relative speed of the objects which moves in the same direction, this incorporates the speed of the object, distance covered by the object, time taken by the object.
Time taken by the man is given by the formula:
$\Rightarrow v = \dfrac{d}{t}$
Where, $v$ denotes the speed by which the man moves, $d$ denotes the distance covered by the man, $t$ denotes the time taken by the man to walk up the moving escalator.

Complete step by step answer
The data given in the problem are as follows;
Time taken by the to walk up a stationary escalator is, $t = 90\,\,s$.
Time taken by the to walk up a moving escalator is, $t = 60\,\,s$.
The distance travelled by the man in the escalator is, $d$
For a stationary escalator:
$\Rightarrow v' = \dfrac{d}{t}$
Where, $v'$ the speed of the man in the stationary escalator.
Substitute the value of the time taken for the man in a stationary escalator in the above formula;
$\Rightarrow v' = \dfrac{d}{{90}}$
For moving escalator:
$\Rightarrow v'' = \dfrac{d}{t}$
Where, $v''$ the speed of the man in the moving escalator.
Substitute the value of the time taken for the man in a moving escalator in the above formula;
$\Rightarrow v'' = \dfrac{d}{{60}}$
Relative velocity:
The relative velocity of the escalator is;
$\Rightarrow v = v' + v''$
$\Rightarrow v = \dfrac{d}{{90}} + \dfrac{d}{{60}}$
By taking the L.C.M. and adding we get;
$\Rightarrow v = \dfrac{{2d + 3d}}{{180}}$
$\Rightarrow v = \dfrac{{5d}}{{180}}$
$\Rightarrow v = \dfrac{d}{{36}}$
From the given main formula;
$\Rightarrow v = \dfrac{d}{t}$
$\Rightarrow t = 36\,\,s$
Therefore, the time taken by the man to walk up the moving escalator is calculated as $t = 36\,\,s$.
Hence the option (C) $t = 36\,\,s$ is the correct answer.

Note
The idea of relative speed is utilized when two or more objects of mass travelling with any speeds are taken into account. That is, one object may be stationary, that is the speed of the object is zero and the speed of the other body with respect to the stationary object is not equal to zero.