Distance, Speed, and Time: The Formulas and the Average-Speed Trap

Why the Average Is Lower

Average speed is total distance divided by total time. You spend more time at the slower speed, so it carries more weight. When the distances at each speed are equal, the correct average is the harmonic mean: 2 × v₁ × v₂ ÷ (v₁ + v₂) = 2 × 60 × 40 ÷ 100 = 48 mph. If the times at each speed are equal (for example, 1 hour at 60 mph and 1 hour at 40 mph), then the simple average of 50 mph is correct, since the total distance is 100 miles in 2 hours.

The rule: average over equal distances means the harmonic mean; average over equal times means the arithmetic mean.

Meeting and Catching Up

Two trains start 300 miles apart and travel toward each other at 70 and 80 mph. Their closing speed is 150 mph, so they meet after 300 ÷ 150 = 2 hours. If a car leaves at 60 mph and a second car leaves one hour later at 75 mph on the same road, the first car has a 60-mile head start. The second car closes the gap at 15 mph, so it catches up after 60 ÷ 15 = 4 hours, at which time it has traveled 300 miles. When objects move toward each other, add their speeds; when one chases another in the same direction, subtract.

Unit Conversions

Keep units consistent. Distance in kilometers and speed in km/h give time in hours. To convert 90 km/h to meters per second, divide by 3.6: 25 m/s. To convert 60 mph to feet per second, multiply by 1.4667: 88 ft/s. Minutes need conversion: 150 miles at 50 mph takes 3 hours, but 150 miles at 55 mph takes 2.73 hours, or 2 hours 44 minutes (0.73 × 60 = 43.6). A common mistake is to treat the decimal part of hours as minutes: 2.73 hours is not 2 hours 73 minutes.

Time Savings From Driving Faster

Raising your speed saves less time than most people expect, especially on shorter trips. A 60-mile trip at 60 mph takes 60 minutes; at 70 mph, 51.4 minutes, saving 8.6 minutes; at 80 mph, 45 minutes, saving 15 minutes. The relationship is hyperbolic: each additional 10 mph saves less than the previous one. At the same time, fuel consumption and risk rise rapidly with speed, since aerodynamic drag grows with the square of speed. Use time = distance ÷ speed to compare the benefit and cost before choosing to rush.

Using These Ideas

Estimate travel times from a map distance and a realistic average speed, including stops and traffic. For flights, add boarding, taxi, and ground transport. For a long drive, plan for breaks: a 500-mile drive at 60 mph is 8.3 hours of driving, but with 2 hours of stops, it takes over 10 hours. Check estimates using the harmonic mean when segments have different speeds over equal distances.