The Slower Segment Wins

Averaging speeds is where most people slip. Drive 60 miles at 30 mph, then 60 miles at 60 mph, and your average is not 45 mph but 40 mph. The slow leg takes two hours, the fast leg one hour: 120 miles in 3 hours = 40 mph.

This is the harmonic mean, and it governs every rate-averaging problem: fuel economy across trips, processing speeds in computing, the effective cost of mixed-price purchases. The rule to remember: when averaging rates, use total-over-total, never the simple mean of the rates themselves.