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

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MindYourDecisions
Published at : 10 Jan 2021
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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?

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

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

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