smanstar wrote:Escalator is moving from first floor to ground floor in a shopping complex. Jack took 30 seconds to reach the ground floor if he takes 25 steps but if he triples his speed it takes him only 18 seconds .
a) Total steps in the stationary escalator.
b) Time taken if only the escalator was in motion
Let e = the escalator's rate.
Case 1: time = 30 seconds.
Since Jack takes 25 steps in 30 seconds, his rate = 25/30 = 5/6 steps per second.
Combined rate for Jack and the escalator = 5/6 + e.
Number of steps traveled = r*t = (5/6 + e)(30) = 25 + 30e.
Case 2: time = 18 seconds.
Since Jack triples his speed, his rate = 3(5/6) = 5/2 steps per second.
Combined rate for Jack and the escalator = 5/2 + e.
Number of steps traveled = r*t = (5/2 + e)(18) = 45 + 18e.
Since the number of steps between the first floor and the ground floor is the same in each case, we get:
25 + 30e = 45 + 18e
12e = 20
e = 20/12 = 5/3 steps per second.
Referring to case 1:
Number of steps traveled = (5/6 + 5/3)(30) = 25 + 50 = 75 steps.
Since the escalator's rate = 5/3 steps per second, the time for the escalator alone = 75/(5/3) = 45 seconds.
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