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average speed — Definition, Formula & Examples

Average speed is the total distance traveled divided by the total time taken for the entire trip. It gives you a single speed that represents the whole journey, even if you moved at different speeds along the way.

For a journey consisting of one or more segments, the average speed is defined as the ratio of the cumulative distance covered across all segments to the cumulative elapsed time across all segments. Unlike an arithmetic mean of individual speeds, average speed weights each speed by the time (or distance) spent at that speed.

Key Formula

Average Speed=Total DistanceTotal Time\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}
Where:
  • Total Distance\text{Total Distance} = Sum of all distances traveled across every segment of the trip
  • Total Time\text{Total Time} = Sum of all time intervals across every segment of the trip

How It Works

To find average speed, add up every part of the distance traveled, then add up every part of the time spent, and divide the total distance by the total time. This works whether you drove on a highway, sat in traffic, or even stopped for lunch — all of it counts. A classic exam trap involves a round trip at two different speeds: you cannot simply average the two speeds. Instead, you must compute total distance and total time separately, then divide.

Worked Example

Problem: A car drives 60 miles at 30 mph, then drives 60 miles at 60 mph. What is the average speed for the whole trip?
Find the time for each segment: Segment 1: 60 miles at 30 mph. Segment 2: 60 miles at 60 mph.
t1=6030=2 hours,t2=6060=1 hourt_1 = \frac{60}{30} = 2 \text{ hours}, \quad t_2 = \frac{60}{60} = 1 \text{ hour}
Find total distance and total time: Add the distances and times from both segments.
Total Distance=60+60=120 miles,Total Time=2+1=3 hours\text{Total Distance} = 60 + 60 = 120 \text{ miles}, \quad \text{Total Time} = 2 + 1 = 3 \text{ hours}
Divide total distance by total time: Apply the average speed formula.
Average Speed=1203=40 mph\text{Average Speed} = \frac{120}{3} = 40 \text{ mph}
Answer: The average speed is 40 mph — not 45 mph, which would be the incorrect simple average of 30 and 60.

Another Example

Problem: A runner jogs 2 km in 10 minutes, rests for 5 minutes, then jogs another 1 km in 5 minutes. What is the runner's average speed in km per minute?
Total distance: Add all distances, including the rest segment where distance is 0.
2+0+1=3 km2 + 0 + 1 = 3 \text{ km}
Total time: Include the rest time — the clock does not stop.
10+5+5=20 min10 + 5 + 5 = 20 \text{ min}
Calculate average speed: Divide total distance by total time.
Average Speed=320=0.15 km/min\text{Average Speed} = \frac{3}{20} = 0.15 \text{ km/min}
Answer: The runner's average speed is 0.15 km/min (or 9 km/h).

Visualization

Why It Matters

Average speed problems appear regularly on standardized tests like the SAT, ACT, and state math exams, where the "just average the two speeds" trap catches many students. In physics courses, understanding average speed builds a foundation for studying velocity, acceleration, and motion graphs. Professionals in logistics and transportation use average speed calculations daily to estimate delivery times and fuel costs.

Common Mistakes

Mistake: Averaging the individual speeds instead of using total distance over total time
Correction: The arithmetic mean of speeds is only correct when equal time is spent at each speed. For equal-distance segments (the most common exam setup), you must calculate the time for each segment first, then use total distance ÷ total time.
Mistake: Forgetting to include rest or stop time in the total time
Correction: Average speed covers the entire trip from start to finish. Any time the clock is running — including breaks, red lights, or pit stops — must be added to the total time in the denominator.

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