To calculate the average race speed, you should convert each race time to a speed and then average the speeds (Option B). Here's why:
Option A: If you were to average the times and then convert that single time figure to a speed, it would not give an accurate representation of the average race speed. This is because averaging times does not account for the varying distances of each race, which would lead to incorrect results. The average of times does not necessarily translate to the average of speeds.
Option B: To calculate the average race speed accurately, you need to calculate the speed for each race individually and then average those speeds. To do this, you would divide the distance of each race by its corresponding time to get the speed for that race. After calculating the speeds for all the races, you can then find the average of those speeds to determine the average race speed.
Here's an example to illustrate the process:
Race 1: Distance = 10 miles, Time = 2 hours Race 2: Distance = 5 miles, Time = 1 hour Race 3: Distance = 8 miles, Time = 1.5 hours
Convert each time to speed: Race 1: Speed = 10 miles / 2 hours = 5 miles per hour Race 2: Speed = 5 miles / 1 hour = 5 miles per hour Race 3: Speed = 8 miles / 1.5 hours = 5.33 miles per hour
Average Speed = (5 mph + 5 mph + 5.33 mph) / 3 = 5.11 miles per hour
Therefore, the average race speed in this example would be 5.11 miles per hour, which accurately reflects the average performance across the races.