Question

A person climbed up a stopped escalator in the 60s. If standing on the same escalator but escalator running up with constant velocity, he takes 40s. How much time is taken by the person to walk up in the moving escalator?
(A) 37s
(B) 27s
(C) 24s
(D) 45s

Answer 1

This problem can be solved with the simple formula of speed= distance/time. Since the distance, that is, the length of the escalator is constant in this problem; we can make use of this, to calculate the time taken by the man to walk up the escalator.
Formula Used:
Speed=$\dfrac{\text{Distance}}{Time}$

Complete answer:
Given,
Time taken for the person to climb the stopped escalator = 60 s
Time taken for person if the escalator is moving at constant speed = 40 s
To find: The time taken by the person to walk up the moving escalator
Let us consider that the distance or the total length of the escalator is D.
$\because $ The time taken by the man to go up the stopped escalator = 60 seconds
$\therefore $ The speed of the person = $\dfrac{D}{60}$
$\because $ The time taken by the man to go up the moving escalator = 40 seconds
\[\therefore \] The speed of the escalator = $\dfrac{D}{40}$
Total speed = $\dfrac{D}{60}+\dfrac{D}{40}$
\[\Rightarrow \]Total speed =\[\dfrac{D}{24}\]
\[\therefore \] The total time taken = $\dfrac{D}{{}^{D}/{}_{24}}$
\[\Rightarrow \] Time taken by the person to walk up the moving escalator = 24 seconds

Therefore the correct answer is (C) 24 seconds.

Additional Information:
The simple relation between distance, speed and time has many applications that we can think of. Problems like these can be attempted by making use of that formula. It is the same with velocity, but in that formula, distance will be replaced by displacement.

Note:
In this problem, we must keep in mind that we need to find the total time in seconds and not the distance or the speed of the person, but if asked, even that can be calculated with appropriate given data.