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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Comments
I geuss he runs super duper fast. I don't know about you, but it takes me about 1/2 second per step to run up. You should have said something about neglecting the time it took for him to run up the step. Also with the escalator as he is running up it he will go up a little more than the number of steps he ran. Something like 4 steps = 4.5 actual distance. 16 steps = 18 actual distance. This is a poorly written MATH problem with good intent. You need to neglect a lot of stuff without being told to neglect it.
I am so sorry. I feel like an idiot now. If you measure the time it took from the start (before running) to the time you get off the escalator. The time it took to run up the steps is neglected because it is already included. I was thinking you run up and then start timing; that would be a little more complicated. Good teaser, just not clear.
Nice one! I've added it to my favourites. You can do it by Algebra but the power of the purely logical solution derived from the difference in times running up is delightfully simple!
Rather than logic, this is math: a simple system of two linear equations with two unknowns.
that was a very confusing teaser, but otherwise very good.
Awsome Should be a math problem though
actually, fasil was right with first comment: this solution is only valid if you think that Mad Ade has infinite speed (insta-run). If we say that elevator speed (in stairs per second) is Ve, and Mad Ade speed of running (in stairs per second) is Va, and if N= number of visible stairs, then we have from first statement: 40= 8/(Ve+Va)+ (N-/Ve , and from second statememnt we have 22.5= 15/(Ve+Va)+ (N-15)/Ve . Now, this two formular really result in N/Ve=60 -> and since N/Ve= time needed to reach top without any running, first part of answer is correct. But second part is NOT correct, unless Va=infinite (ie, for N=24; Va=inf) . More real solutions are: (N=21; Va=2.45), (N=22; Va=4.03), (N=23; Va=8.82) ... and I guess running 2-3 steps in second is most realistic (ie N=21)
Me First Hard One i feeneeshed!!!Pretty easy, didn't know why they say it's hard?
Nice!! The comments about needing to neglect the time it takes to run up a step is valid though - without neglecting this it is impossible to determine the number of steps...
nenad, call the stair you step onto at the bottom stair 1, the next one up stair 2, etc. If you run up 8 stairs to stair 9, your will get to the top when stair 9 gets to the top. It doesn't matter how long it took you to get to stair 9.
nenad, you're equations are wrong because you assume a constant number (N-8 or N-15) to be divided by Ve. The slower Va is, the fewer steps need to be travelled at Ve -- because the escalator moves up as he runs..
i found it super easy - didn't even bother calculating the number of stairs.
i subtracted the 22.5 from 40 seconds, found 17.5, and added that to the 40 seconds which came to 57.5 (and left only one "running" step to work out), divded 17.5 by 7 to get 2.5 (which is how long each individual step in the 17.5 took), and added that to 57.5 to get 60 seconds
i subtracted the 22.5 from 40 seconds, found 17.5, and added that to the 40 seconds which came to 57.5 (and left only one "running" step to work out), divded 17.5 by 7 to get 2.5 (which is how long each individual step in the 17.5 took), and added that to 57.5 to get 60 seconds
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