Brain Teasers
Mad Ade's Escalator Journey
Mad Ade once had a job working in the famous Madadian department store "Horrids".
He used the stores escalator on a daily basis as he skived from duty to duty.
He noticed on one particularly boring day that if he ran up 8 stairs of the escalator from the bottom step, the journey to the top took exactly 40 seconds.
On a later escalator trip he noticed that if he ran up 15 stairs of the escalator the journey time decreased to only 22.5 seconds.
Knowing this, how long would it take Mad Ade to complete the full journey if he did not run up any stairs at all?
Can you work out how many steps of the escalator are actually visible at any one time?
He used the stores escalator on a daily basis as he skived from duty to duty.
He noticed on one particularly boring day that if he ran up 8 stairs of the escalator from the bottom step, the journey to the top took exactly 40 seconds.
On a later escalator trip he noticed that if he ran up 15 stairs of the escalator the journey time decreased to only 22.5 seconds.
Knowing this, how long would it take Mad Ade to complete the full journey if he did not run up any stairs at all?
Can you work out how many steps of the escalator are actually visible at any one time?
Answer
It takes Mad Ade 60 seconds to reach the top, and there are 24 steps visible on the escalator when it's stationary.Running up 7 more steps reduces the time by 17.5 seconds, so running up 1 step reduces the time by 2.5 seconds, so each step takes 2.5 seconds.
So the escalator cycles through 24 steps on a complete trip from base to top. To illustrate:
8+(40/2.5)=24 steps
15+(22.5/2.5)=24 steps
The escalator cycles through all 24 steps in 24(2.5)=60 seconds
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