An escalator in a department store moves down at the rate of 64 steps per minute. Julie can walk fast up ordinary steps at the rate of 96 steps per minute. In the store, there are 48 steps from one level to another. Julie decides to walk fast up the down escalator. How long in seconds will it take her to go up one level?
Let t be the time.
Since Julie's and the escalator's rates are on opposite directions, we can represent it as one of them (+) and the other (-).
Rate is distance traveled over time, or
r = d/t
or solving for d,
d = r*t
Then we write the equation:
(Julie's distance) - (Escalator distance) = (Distance of one level)
96*t - 64*t = 48
32t = 48
t = 1.5 minutes
Hope this helps~ `u`
90 seconds
To find the time it will take Julie to go up one level, we need to determine the relative speed between Julie and the escalator.
Since the escalator moves down at a rate of 64 steps per minute, the relative speed between Julie and the escalator is the difference between their individual speeds.
Julie's speed is 96 steps per minute, and the escalator moves down at a rate of 64 steps per minute. Therefore, the relative speed between Julie and the escalator is 96 - 64 = 32 steps per minute.
Since there are 48 steps from one level to another, Julie needs to cover the distance of 48 steps. To calculate the time it will take her to cover that distance, we can use the formula:
Time = Distance / Speed
Plugging in the values, we get:
Time = 48 steps / 32 steps per minute
Simplifying this equation, we find:
Time = 1.5 minutes
To convert minutes to seconds, we multiply by 60 since there are 60 seconds in one minute:
Time = 1.5 minutes * 60 seconds per minute
Thus, it will take Julie 90 seconds to go up one level.