Escalator problem
How to solve the following question A man can walk up a moving 'up' escalator in 30s. The same man can walk down this moving 'up' escalator in 90s. Assume that his walking speed is same upwards and downwards. How much time will he take to walk up the escalator, when its not moving? a. 30s
b. 45s
c. 60s
d. 90s Thanks Praks
sorry correct ans is 45 sec
speed of man is twice that of escalator's
it can be assumed that speed of man is greater than that of escalator
distance is same v+u = x/30 and v-u = x/90
thus v+u / v-u = 3 or v/u =t then t+1/t-1=3
2t/2=3+1/(3-1) thus t = 2 or speed of the elevator is 2 times the man speed.
Now 3u/u=t'/30 or t'=90 sec is answer.
as speed x time = distance
so speed is inversely proportional to time
speed of goin up/speed of goin down = time to go down/time to go up
hence speed of goin up = 3 * speed of goin down
now speed of man+speed of elevator = speed of goin up
and speed of man - speed of elevator = speed of goin down
so man's speed is twice the elevator speed
hence
2/3=30/x
whre x is time needed to move up if escalator is stoppd
so x=45
i guess the answer is 90 as it has been asked for time taken by man to walk on the escalator which is stagnant......if it would have been asked for the time taken by escator then the answer might be 45 sec....
There is no question of the option d, as it logically points that his speed should be less than 90 and more than 45 so either b or c is correct :P
The solution according to me is correct. (for and to be 45sec)
n/a
let the speed of man = U
let the speed of esc = v
D/(u+v)=30
D/(u+v)=90
u=2v
Implies, D/(3v)=30 (i,e, v=D/90)
now, v=0
D/U=D/2v=45 sec
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90 sec is the correct answer
as speed of escalator is twice that of man's