How Crossed Ladders And Working Together Problems Are Related – The Harmonic Mean

Problem 1: Two ladders are criss-crossed against walls of height 3 and 5. At what height do they intersect? Problem 2: I take 3 hours to complete a job, and you take 5 hours to do the same job. How long does it take if we work together? This video demonstrates that both problems have the same answer–equal to half of the harmonic mean–and the two answers are related geometrically!

The “working together” problem also has an algebraic solution:

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