Suppose someone drives a car from one city to another and you are asked to calculate the average speed, in miles per hour, that the car traveled. The information you are given can influence how you approach the problem. As long as you can determine the total distance traveled and the total time spent traveling, you can calculate the car's average speed using a simple formula.
What Is an Average?
An average is a calculation that reveals what is the central or most common number in a set of numbers. For example, you might say that the average age of all high school students is sixteen years old. This is the central value in the age range of 14 to 18 years old to which most high school students belong.
The Formula for Average Speed
To calculate any average, you add up all the numbers in a set and divide the sum by the number of numbers in the set. Though it can be done that way, calculating average speed is usually a little different from calculating most other averages. To calculate average speed, you typically divide the total distance traveled by the total amount of time spent traveling. Even though a car might have been traveling at different speeds over parts of the overall distance, the total time part of the calculation accounts for that. The formula for average speed looks like this:
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Average speed = total distance ÷ total time
Calculating Average Speed From Total Distance and Total Time
Imagine someone drives a car from City A to City B. If you know that the two cities are 350 miles apart and the trip took six hours, you can simply plug those values into the formula for average speed, like so:
Average speed = 350 miles ÷ 6 hours = 58.3 miles/hour
The answer tells you that the car traveled at an average speed of 58.3 miles per hour. The car was likely traveling faster at times and slower at other times, with 58.3 miles per hour being the central or most common speed.
Calculating Average Speed From Multiple Distances and Times
You can still make the calculation if given multiple distances and times. Suppose you are told a driver made the trip between City X and City Y over three days, with each day's drive described as follows:
Day 1: The driver left City X and drove 100 miles in three hours. Day 2: The driver drove 250 miles in four hours. Day 3: The driver drove 300 miles in five hours and arrived at City Y.
The easiest way to calculate average speed in this case is to sum all the distances in the top part of the average speed equation and sum all the times in the bottom part, like so:
Average speed = (100 miles + 250 miles + 300 miles) ÷ (3 hours + 4 hours + 5 hours) = 650 miles ÷ 12 hours = 54.2 miles/hour
The driver's average speed on this trip was 54.2 miles per hour.