Here's my solution to the escalator problem in my previous post.
Per minute, I climb n steps and the escalator moves along by s steps. So relative to the bottom of the escalator I am travelling at the rate of n + s steps per minute.
If there are p 'visible steps' on the escalator and I take t minutes to get to the top, then t = p/(n + s).
But in t minutes I actually climb nt of the moving steps. This is the variable I call m, the actual number of steps that I take in getting to the top.
So m = nt = np/(n + s).
So below is my formula!
m = np/(n + s).
I must admit I never expected it to be as complicated as this.
To understand this formula, think of it as saying that the proportion of visible steps I climb is the ratio of my speed (n) to the sum of my speed and the speed of the escalator (n + s).
For example, if the escalator has 30 'visible steps' and is moving at 90 steps per minute, my speed is 120 steps per minute, then the proportion of the 30 steps I will tread on will be 120/210, or 4/7 of them, which is about 17.
If you plot m against n, from n = 0, you get a curve that starts at the origin (m = 0) and tends to p as n tends to infinity.
When n = s, notice that m = s/2, which makes sense intuitively: if I climb at the same rate as the escalator is moving I will cover half the steps before I get to the top.
Note also that as n increases the gain in my step count decreases. For example, with a 30-step escalator, and a speed of 90 steps rising per minute ...
When n = 0, m = 0
When n = 60, m = 12
When n = 120, m = 17
When n = 180, m = 20
When n = 240, m = 22
When n = 300, m = 23
It's intriguing to think about how the graph behaves for values of n less than zero down to n = –s. These values of n correspond to walking down the escalator when it is going up. Provided you walk down slower than the escalator is going up, then you will get to the top! The number of steps you take, m, will turn out to be negative because you are walking down the escalator. If you walk down as fast as the escalator is going up (n = –s) then the formula involves division by zero, which is impossible: you never get to the top. In fact, you never get anywhere.
You can have even more fun now, by thinking about how the formula works for climbing up an escalator going down!
Sunday, 20 November 2016
Subscribe to:
Post Comments (Atom)
Nice it seems to be good post... It will get readers engagement on the article since readers engagement plays an vital role in every blog.i am expecting more updated posts from your hands.
ReplyDeleteCloud Computing Training in Chennai
IEEE Final Year Project centers make amazing deep learning final year projects ideas for final year students Final Year Projects for CSE to training and develop their deep learning experience and talents.
DeleteIEEE Final Year projects Project Centers in India are consistently sought after. Final Year Students Projects take a shot at them to improve their aptitudes, while specialists like the enjoyment in interfering with innovation.
corporate training in chennai corporate training in chennai
corporate training companies in india corporate training companies in india
corporate training companies in chennai corporate training companies in chennai
I have read your blog its very attractive and impressive. I like it your blog. Digital Marketing Company in Chennai
nice post.
ReplyDeletewe are hospital lift service providers in delhi
goods lift manufacturers in delhi
glass lift service providers in delhi
residential elevator service providers in delhi
Thanks for the informative article.This is one of the best resources I have found in quite some time.Nicely written and great info.I really cannot thank you enough for sharing.
ReplyDeleteHerbalife in Chennai
Subamwellness in Chennai
Weight Loss in Chennai
Weight Gain in Chennai
This looks absolutely perfect. All these tiny details are made with lot of background knowledge. I like it a lot.
ReplyDeletepython course in pune
python course in chennai
python course in Bangalore
thanks for giving that type of information. ielts coaching in gurgaon
ReplyDeleteGood Post! Thank you so much for sharing this pretty post, it was so good to read and useful to improve my knowledge as updated one, keep blogging.
ReplyDeleterpa training in chennai
rpa training in bangalore
rpa course in bangalore
best rpa training in bangalore
rpa online training
Inspiring writings and I greatly admired what you have to say , I hope you continue to provide new ideas for us all and greetings success always for you..Keep update more information..
ReplyDeleteJava training in Pune
Java interview questions and answers
Java training in Chennai | Java training institute in Chennai | Java course in Chennai
Java training in Bangalore | Java training institute in Bangalore | Java course in Bangalore
Nice tutorial. Thanks for sharing the valuable information. it’s really helpful. Who want to learn this blog most helpful. Keep sharing on updated tutorials…
ReplyDeleteBest Devops training in sholinganallur
Devops training in velachery
Devops training in annanagar
Devops training in tambaram
Fantastic work! This is the type of information that should follow collective approximately the web. Embarrassment captivating position Google for not positioning this transmit higher! Enlarge taking place greater than and visit my web situate
ReplyDeleteData Science course in kalyan nagar | Data Science Course in Bangalore
Data Science course in OMR | Data Science Course in Chennai
Data Science course in chennai | Best Data Science training in chennai
Data science course in velachery | Data Science course in Chennai
Data science course in jaya nagar | Data Science course in Bangalore
Data Science interview questions and answers
When I initially commented, I clicked the “Notify me when new comments are added” checkbox and now each time a comment is added I get several emails with the same comment. Is there any way you can remove people from that service? Thanks.
ReplyDeleteAdvanced AWS Training in Bangalore | Amazon Web Services Training in Bangalore
Amazon Web Services Training in Pune | Best AWS Training in Pune
AWS Online Training | Online AWS Certification Course - Gangboard
Top 110 AWS Interview Question and Answers | Advanced AWS interview Questions and Answers – AWS jobs
Excellent blog!!!Thanks for sharing. Keep doing more.
ReplyDeleteLanguage School Franchise
English Language School Franchise
Computer Education Franchise In India
Language Education Franchise
Computer Education Franchise
Education Franchise India
Computer Center Franchise
I am really enjoying reading your well written articles.
ReplyDeleteIt looks like you spend a lot of effort and time on your blog.Keep Doing.
data analysis courses in bangalore
Data Science Training Institutes in Bangalore
Data Science Certification Bangalore
best analytics courses in bangalore
best data analytics courses in bangalore
big data analytics certification in bangalore
Wonderful blog.. Thanks for sharing informative Post. Its very useful to me.
ReplyDeleteArticle submission sites
Guest posting sites
Well Said, you have furnished the right information that will be useful to anyone at all time. Thanks for sharing your Ideas.
ReplyDeleteangularjs Training in btm
angularjs Training in electronic-city
angularjs online Training
angularjs Training in marathahalli
angularjs interview questions and answers
This is a nice article here with some useful tips for those who are not used-to comment that frequently. Thanks for this helpful information I agree with all points you have given to us. I will follow all of them.
ReplyDeleteDevops Training in Bangalore
Best Devops Training in pune
I'm here representing the visitors and readers of your own website say many thanks for many remarkable.
ReplyDeleteData science course in bangalore
Thanks for the informative article. This is one of the best resources I have found in quite some time. Nicely written and great info. I really cannot thank you enough for sharing.
ReplyDeletemicrosoft azure training in bangalore
rpa training in bangalore
best rpa training in bangalore
rpa online training
Thanks for sharing informative post.
ReplyDeleteCustomer relationship management Software in chennai
CRM software in chennai
CRM software in us
erp in chennai
crm software development services in us
crm software development in us
english to hindi typing
ReplyDeleteI would definitely thank the admin of this blog for sharing this information with us. Waiting for more updates from this blog admin.
ReplyDeleteBlue Prism Training in Chennai
Blue Prism Training
Azure Training in Chennai
Cloud Computing Training in Chennai
Automation Anywhere Training in Chennai
Blue Prism Training in Anna Nagar
Blue Prism Training in T Nagar
Blue Prism Training in OMR
Blue Prism Training in Porur
For Devops Training in Bangalore Visit:Devops Training in Bangalore
ReplyDeleteThank you for excellent article.Great information for new guy like antimalware service executable
ReplyDeleteNice blog,I understood the topic very clearly,And want to study more like this.
ReplyDeleteData Scientist Course
I feel very grateful that I read this. It is very helpful and very informative and I really learned a lot from it.
ReplyDeletedata science course
Thanks for this valuable information. it is really helpful
ReplyDeletehttps://www.acte.in/angular-js-training-in-chennai
https://www.acte.in/angular-js-training-in-annanagar
https://www.acte.in/angular-js-training-in-omr
https://www.acte.in/angular-js-training-in-porur
https://www.acte.in/angular-js-training-in-tambaram
https://www.acte.in/angular-js-training-in-velachery
It is very useful information.
ReplyDeleteAngularJS training in chennai | AngularJS training in anna nagar | AngularJS training in omr | AngularJS training in porur | AngularJS training in tambaram | AngularJS training in velachery
Thanks for the insightful post
ReplyDeleteSalesforce Training | Online Course | Certification in chennai | Salesforce Training | Online Course | Certification in bangalore | Salesforce Training | Online Course | Certification in hyderabad | Salesforce Training | Online Course | Certification in pune
I must appreciate you for providing such a valuable content for us. This is one amazing piece of article. Helped a lot in increasing my knowledge.
ReplyDeleteAWS training in chennai | AWS training in annanagar | AWS training in omr | AWS training in porur | AWS training in tambaram | AWS training in velachery
After reading your article I was amazed. I know that you explain it very well. And I hope that other readers will also experience how I feel after reading your article.
ReplyDeleteSimple Linear Regression
Correlation vs Covariance
I hope you continue to provide new ideas for us all and greetings success always for you. Keep update more information. It is very helpful and very informative and I really learned a lot from it.
ReplyDeletepython training in chennai
python online training in chennai
python training in bangalore
python training in hyderabad
python online training
python flask training
python flask online training
python training in coimbatore
I just got to this amazing site not long ago. I was actually captured with the piece of resources you have got here. Big thumbs up for making such wonderful blog page!
ReplyDeleteWeb Designing Training in Chennai
Web Designing Course in Chennai
Web Designing Training in Bangalore
Web Designing Course in Bangalore
Web Designing Training in Hyderabad
Web Designing Course in Hyderabad
Web Designing Training in Coimbatore
Web Designing Training
Web Designing Online Training
I have to search sites with relevant information on given topic and provide them to teacher our opinion and the article.
ReplyDeleteSimple Linear Regression
Correlation vs Covariance
Very interesting to read this article.I would like to thank you for the efforts you had made for writing this awesome article. This article inspired me to read more. keep it up.
ReplyDeleteCorrelation vs Covariance
Simple linear regression
data science interview questions
Attend The Data Science Courses From ExcelR. Practical Data Science Courses Sessions With Assured Placement Support From Experienced Faculty. ExcelR Offers The Data Science Courses. data science courses
ReplyDeleteAfter reading your article I was amazed. I know that you explain it very well. And I hope that other readers will also experience how I feel after reading your article.
ReplyDeleteSimple Linear Regression
Correlation vs covariance
KNN Algorithm
Logistic Regression explained
This Was An Amazing ! I Haven't Seen This Type of Blog Ever ! Thankyou For Sharing, data science online course
ReplyDeleteGood Post! , it was so good to read and useful to improve my knowledge as an updated one, keep blogging. After seeing your article I want to say that also a well-written article with some very good information which is very useful for the readers....thanks for sharing it and do share more posts like this.
ReplyDeleteAWS Online Training
Online AWS Certification Training
This is a wonderful article, Given so much info in it, These type of articles keeps the users interest in the website, and keep on sharing more ... good luck.
ReplyDeletedata science interview questions
Wow it is really wonderful and awesome thus it is very much useful for me to understand many concepts and helped me a lot. it is really explainable very well and i got more information from your blog.
ReplyDeleteAngular js Training in Chennai
Angular js Training in Velachery
Angular js Training in Tambaram
Angular js Training in Porur
Angular js Training in Omr
Angular js Training in Annanagar
This blog is very interesting. I learned so much and want to thank you for sharing it in the first place. It is really helpful for my future endeavors. Thanks for your efforts and making it available to public
ReplyDeleteSelenium Training in Chennai
Selenium Training in Velachery
Selenium Training in Tambaram
Selenium Training in Porur
Selenium Training in Omr
Selenium Training in Annanagar
Nice article.
ReplyDeleteamazon web services aws training in chennai
microsoft azure course in chennai
workday course in chennai
android course in chennai
ios course in chennai
Good Post! Thank you so much for sharing this pretty post, it was so good to read and useful to improve my knowledge as updated one, keep blogging.
ReplyDeletesalesforce training in chennai
software testing training course in chennai
robotic process automation rpa training in chennai
blockchain training in chennai
devops training in chennai
Oracle Corporation is an American multinational computer technology corporation headquartered in Redwood Shores, California.
ReplyDeletetally training in chennai
hadoop training in chennai
sap training in chennai
oracle training in chennai
angular js training in chennai
Highly appreciable regarding the uniqueness of the content. This perhaps makes the readers feels excited to get stick to the subject. Certainly, the learners would thank the blogger to come up with the innovative content which keeps the readers to be up to date to stand by the competition. Once again nice blog keep it up and keep sharing the content as always.
ReplyDeleteData Science Training
Highly appreciable regarding the uniqueness of the content. This perhaps makes the readers feels excited to get stick to the subject. Certainly, the learners would thank the blogger to come up with the innovative content which keeps the readers to be up to date to stand by the competition. Once again nice blog keep it up and keep sharing the content as always.
ReplyDeleteData Science Course in Bhilai
Fantastic blog extremely good well enjoyed with the incredible informative content which surely activates the learners to gain the enough knowledge. Which in turn makes the readers to explore themselves and involve deeply in to the subject. Wish you to dispatch the similar content successively in future as well.
ReplyDeleteData Science training in Raipur
Thankyou for the wonderful content and knowledge. It was really Helpful. # BOOST Your GOOGLE RANKING.It’s Your Time To Be On #1st Page
ReplyDeleteOur Motive is not just to create links but to get them indexed as will
Increase Domain Authority (DA).We’re on a mission to increase DA PA of your domain
High Quality Backlink Building Service
1000 Backlink at cheapest
50 High Quality Backlinks for just 50 INR
2000 Backlink at cheapest
5000 Backlink at cheapest
It was rally fun reading your article. Thankyou for such a wonderful article. # BOOST Your GOOGLE RANKING.It’s Your Time To Be On #1st Page
ReplyDeleteOur Motive is not just to create links but to get them indexed as will
Increase Domain Authority (DA).We’re on a mission to increase DA PA of your domain
High Quality Backlink Building Service
Boost DA upto 15+ at cheapest
Boost DA upto 25+ at cheapest
Boost DA upto 35+ at cheapest
Boost DA upto 45+ at cheapest
Wow, amazing post! Really engaging, thank you.
ReplyDeletePython Training In Bangalore
Python Training Institute In Bangalore
Thanks for posting the best information and the blog is very helpful.data science interview questions and answers
ReplyDeleteIt is so nice article thank you for sharing this valuable content.
ReplyDeleteworkday online training hyderabad
workday online training in india
coin haber - koin haber - kripto para haberleri - coin haber - instagram video indir - instagram takipçi satın al - instagram takipçi satın al - tiktok takipçi satın al - instagram takipçi satın al - instagram takipçi satın al - instagram takipçi satın al - instagram takipçi satın al - instagram takipçi satın al - binance güvenilir mi - binance güvenilir mi - binance güvenilir mi - binance güvenilir mi - instagram beğeni satın al - instagram beğeni satın al - google haritalara yer ekleme - btcturk güvenilir mi - binance hesap açma - kuşadası kiralık villa - tiktok izlenme satın al - instagram takipçi satın al - sms onay - paribu sahibi kim - binance sahibi kim - btcturk sahibi kim - paribu ne zaman kuruldu - binance ne zaman kuruldu - btcturk ne zaman kuruldu - youtube izlenme satın al - torrent oyun - google haritalara yer ekleme - altyapısız internet - bedava internet - no deposit bonus forex - erkek spor ayakkabı - tiktok jeton hilesi - tiktok beğeni satın al - microsoft word indir - misli indir
ReplyDeletetakipçi satın al
ReplyDeletetakipçi satın al
takipçi satın al
ReplyDeleteI was just examining through the web looking for certain information and ran over your blog.It shows how well you understand this subject. Bookmarked this page, will return for extra. data science course in vadodara
Impressive blog to be honest definitely this post will inspire many more upcoming aspirants. Eventually, this makes the participants to experience and innovate themselves through knowledge wise by visiting this kind of a blog. Once again excellent job keep inspiring with your cool stuff.
ReplyDeleteData Science Training in Bhilai
Wonderful blog found to be very impressive to come across such an awesome blog. I should really appreciate the blogger for the efforts they have put in to develop such an amazing content for all the curious readers who are very keen of being updated across every corner. Ultimately, this is an awesome experience for the readers. Anyways, thanks a lot and keep sharing the content in future too.
ReplyDeleteData Science Course in Bhilai
Extraordinary blog went amazed with the content that they have developed in a very descriptive manner. This type of content surely ensures the participants to explore themselves. Hope you deliver the same near the future as well. Gratitude to the blogger for the efforts.
ReplyDeleteData Science Training
Stupendous blog huge applause to the blogger and hoping you to come up with such an extraordinary content in future. Surely, this post will inspire many aspirants who are very keen in gaining the knowledge. Expecting many more contents with lot more curiosity further.
ReplyDeleteData Science Certification in Bhilai
Extremely overall quite fascinating post. I was searching for this sort of data and delighted in perusing this one. Continue posting. A debt of gratitude is in order for sharing. data scientist course in delhi
ReplyDeleteIt is so nice article thank you for sharing this valuable content.
ReplyDeleteworkday online training hyderabad
workday online training in india
Thanks for sharing valuable information in the article.students can make a good career by learning. We are providing the best services click on below links to visit our website.
ReplyDeleteOracle Fusion HCM Training
Workday Training
Okta Training
Palo Alto Training
Adobe Analytics Training
Thanks for sharing.
ReplyDeletePre Primary Schools in Pune
thanks admin good content HDE Bilişim
ReplyDeleteAlışveriş
Compo Expert
Multitek
Seokoloji
Vezir Sosyal Medya
Adak
Maltepe Adak
I think this is one of the best blog for me because this is really helpful for me. Thanks for sharing this valuable information
ReplyDeleteinternship meaning | internship meaning in tamil | internship work from home | internship certificate format | internship for students | internship letter | Internship completion certificate | internship program | internship certificate online | internship graphic design
I truly appreciate just perusing the entirety of your weblogs. Just needed to educate you that you have individuals like me who value your work. Unquestionably an extraordinary post. Caps off to you! The data that you have given is exceptionally useful.iot course in noida
ReplyDeleteExcellent blog. Keep blogging with us.
ReplyDeleteTamil romantic novels pdf
Ramanichandran novels PDF
srikala novels PDF
Mallika manivannan novels PDF
muthulakshmi raghavan novels PDF
Infaa Alocious Novels PDF
N Seethalakshmi Novels PDF
Sashi Murali Tamil Novels PDF
Excellent Blog! I would like to thank for the efforts you have made in writing this post. I am hoping the same best work from you in the future as well. I wanted to thank you for this websites! Thanks for sharing. Great websites!.iot course in delhi
ReplyDeleteStupendous blog huge applause to the blogger and hoping you to come up with such an extraordinary content in future. Surely, this post will inspire many aspirants who are very keen in gaining the knowledge. Expecting many more contents with lot more curiosity further.
ReplyDeleteData Science Certification in Bhilai
Extraordinary blog went amazed with the content that they have developed in a very descriptive manner. This type of content surely ensures the participants to explore themselves. Hope you deliver the same near the future as well. Gratitude to the blogger for the efforts.
ReplyDeleteData Science Training
Very useful post. This is my first time i visit here. I found so many interesting stuff in your blog especially its discussion. Really its great article. Keep it up.
ReplyDeletedata analytics course in hyderabad
Really awesome blog. Your blog is really useful for me
ReplyDeleteRegards,
ups computer full form
kb full form
love full form
rpm full form
ide full form in computer
dtp full form
d v d full form
bca full form and subjects
swat full form
micr full form in computer
Great post. keep sharing such a worthy information.
ReplyDeleteHadoop Training in Chennai
Great post. Thanks for sharing such a useful blog.
ReplyDeleteSEO Training in T Nagar
SEO Training in Chennai
Superb blog and great post.Its truly supportive for me, anticipating for all the more new post. Continue Blogging!
ReplyDeleteartificial intelligence internship | best final year projects for cse | internship certificate online | internship for mba finance students | internship meaning in tamil
Incredibly in general very entrancing post. I was looking for such an information and savored the experience of scrutinizing this one. Keep posting. An obligation of appreciation is for sharing.data scientist course in bhubaneswar
ReplyDeletetiktok jeton hilesi
ReplyDeletetiktok jeton hilesi
referans kimliği nedir
gate güvenilir mi
tiktok jeton hilesi
paribu
btcturk
bitcoin nasıl alınır
yurtdışı kargo
I at long last discovered incredible post here.I will get back here. I just added your blog to my bookmark locales. thanks.Quality presents is the urgent on welcome the guests to visit the website page, that is the thing that this site page is giving.360digitmg-data science course business analytics course in surat
ReplyDeleteThe blog data is excellent and informative as well
ReplyDeletedata analytics course in hyderabad
Truly overall quite fascinating post. I was searching for this sort of data and delighted in perusing this one. Continue posting. Much obliged for sharing.data science course in bhopal
ReplyDeleteGreat post. keep sharing such a worthy information.
ReplyDeleteWeb Designing Course In Chennai
Much obliged for sharing this brilliant substance. its extremely fascinating. Numerous web journals I see these days don't actually give whatever pulls in others however the manner in which you have plainly clarified everything it's truly awesome. There are loads of posts But your method of Writing is so Good and Knowledgeable. continue to post such helpful data and view my site too...
ReplyDeletehow to make a paper airplane that flies far and straight step by step | classic dart paper airplane | zazoom internet | windfin | how to make the coolest paper airplane | how to make a good paper airplane that flies far | best paper model | the best glider paper airplane | paper airplane aerodynamics | super paper airplanes | how to make easy paper planes | control surfaces on a plane
seo fiyatları
ReplyDeletesaç ekimi
dedektör
instagram takipçi satın al
ankara evden eve nakliyat
fantezi iç giyim
sosyal medya yönetimi
mobil ödeme bozdurma
kripto para nasıl alınır
manaiyadi sasthiram tamil
ReplyDeletefood for hair growth in tamil
moochu pidippu
badam benefits in tamil
உடல் எடை அதிகரிக்க
badam pisin benefits in tamil
dolo 650 uses in tamil
bay leaf in tamil
saibol cream uses in tamil
அதிமதுரம் பயன்கள்
appealing, pronounce. I simply stumbled upon your blog and desired to make known that i have favored surfing your weblog posts. After each, i can definitely subscribe to your feed, and that i purpose you will write within the lower back again soon! Ocam Crack
ReplyDeleteI suppose that is an informative make recognized and it's miles agreed useful and knowledgeable. therefore, i might related to to thank you for the moves which you have made in writing this text. all of the content material is virtually expertly-researched. thank you...SuperantiSpyware Professional Keys
ReplyDelete