Mixed-Speed Problems

Drive 100 miles at 50 mph (2 hours) then 100 miles at 100 mph (1 hour). Total: 200 miles in 3 hours. Average speed is 200 ÷ 3 = 66.7 mph — not 75, which is the simple average of 50 and 100. The slower segment takes longer, so it weighs more heavily.

This is the harmonic mean at work when the two rates apply over equal distances. You cannot just add the speeds and divide, because the slower leg takes more time. For the two equal-distance legs above, the harmonic mean of 50 and 100 is 2/(1/50 + 1/100) = 66.7 mph, which matches total distance divided by total time.