A man can walk up a moving "up" escalator in 30 seconds. The same man can walk down this moving "up" escalator in 90 seconds. Assume that his walking speed is same upwards and downwards. How much time will he take to walk up the escalator, when it is not moving?
Question
A man can walk up a moving "up" escalator in 30 seconds. The same man can walk down this moving "up" escalator in 90 seconds. Assume that his walking speed is same upwards and downwards. How much time will he take to walk up the escalator, when it is not moving?
Solution
Let's denote:
- The length of the escalator as L
- The man's walking speed as W (in length per second)
- The escalator's speed as E (in length per second)
When the man walks up the moving escalator, he is moving at a speed of (W+E), so the time it takes him to cover the length of the escalator is L/(W+E). According to the problem, this time is 30 seconds.
So, we have the equation:
L = 30*(W+E) ...(1)
When the man walks down the moving escalator, he is moving at a speed of (W-E), so the time it takes him to cover the length of the escalator is L/(W-E). According to the problem, this time is 90 seconds.
So, we have the second equation:
L = 90*(W-E) ...(2)
Now, we can solve these two equations to find the values of W and E.
By dividing equation (1) by equation (2), we get:
30*(W+E) / 90*(W-E) = 1
Solving this equation gives us:
W = 2E
Now, we can substitute W = 2E into equation (1) to find the value of E:
L = 30*(2E+E)
L = 90E
So, E = L/90
Substituting E = L/90 into W = 2E gives us:
W = 2*(L/90)
W = L/45
Now, when the escalator is not moving, the man is moving at a speed of W to cover the length of the escalator, so the time it takes him is L/W. Substituting W = L/45 gives us:
Time = L / (L/45)
Time = 45 seconds
So, the man will take 45 seconds to walk up the escalator when it is not moving.
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