Which Is Faster: Run Half The Distance Or Half The Time?

Thanks to Muztoba Ali in Bangladesh for this problem! Two brothers, A and B, have the exact same walking speed and the exact same running speed. One day they started the same trip to the same place. Brother A walked for half of the distance and ran the rest while brother B walked for half of the time and ran for the other half of time. Which brother reached the end of the trip first?

My blog post for this video
https://wp.me/p6aMk-81z

AM-HM Inequality proved geometrically:
https://youtu.be/iKcqSrHvdHM

AM-HM proved algebraically
https://proofwiki.org/wiki/Arithmetic_Mean_Never_Less_than_Harmonic_Mean

Playlist to watch all videos on MindYourDecisions

This is the only channel to feature math topics suggested by people from around the world. Sadly some textbooks, websites, and other channels think math is limited to specific topics from certain countries–and they are vocal about it. Support the channel on Patreon so we can prove math really is universal:
https://www.patreon.com/mindyourdecisions

If you buy from the links below I may receive a commission for sales. This has no effect on the price for you.

My Books
“The Joy of Game Theory” shows how you can use math to out-think your competition. (rated 4/5 stars on 34 reviews)
http://amzn.to/1uQvA20

“The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias” is a handbook that explains the many ways we are biased about decision-making and offers techniques to make smart decisions. (rated 4.6/5 stars on 3 reviews)
http://amzn.to/1o3FaAg

“Math Puzzles Volume 1” features classic brain teasers and riddles with complete solutions for problems in counting, geometry, probability, and game theory. Volume 1 is rated 4.4/5 stars on 13 reviews.
http://amzn.to/1GhUUSH

“Math Puzzles Volume 2” is a sequel book with more great problems. (rated 4.3/5 stars on 4 reviews)
http://amzn.to/1NKbyCs

“Math Puzzles Volume 3” is the third in the series. (rated 4/5 stars on 6 reviews)
http://amzn.to/1NKbGlp

“40 Paradoxes in Logic, Probability, and Game Theory” contains thought-provoking and counter-intuitive results. (rated 4.4/5 stars on 13 reviews)
http://amzn.to/1LOCI4U

“The Best Mental Math Tricks” teaches how you can look like a math genius by solving problems in your head (rated 4.8/5 stars on 5 reviews)
http://amzn.to/18maAdo

“Multiply Numbers By Drawing Lines” This book is a reference guide for my video that has over 1 million views on a geometric method to multiply numbers. (rated 5/5 stars on 4 reviews)
http://amzn.to/XRm7M4

Connect with me
My Blog: https://mindyourdecisions.com/blog/
Twitter: https://twitter.com/preshtalwalkar
Facebook: https://www.facebook.com/pages/Mind-Your-Decisions/168446714965
Google+: https://plus.google.com/108336608566588374147/posts
Pinterest: https://www.pinterest.com/preshtalwalkar/
Tumblr: https://preshtalwalkar.tumblr.com/
Instagram: https://instagram.com/preshtalwalkar/
Patreon: https://www.patreon.com/mindyourdecisions

Newsletter (sent only for big news, like a new book release): http://eepurl.com/KvS0r