To determine Harvey's average speed in kilometers per hour, we will follow these steps:
1. Convert the distance to an improper fraction or decimal: Harvey can run [tex]\(3 \frac{1}{6}\)[/tex] kilometers.
Let's convert this mixed number into an improper fraction first:
[tex]\[
3 \frac{1}{6} = 3 + \frac{1}{6} = \frac{18}{6} + \frac{1}{6} = \frac{19}{6}
\][/tex]
Alternatively, we can convert it directly to a decimal:
[tex]\[
3 \frac{1}{6} = 3 + 0.16666666666666666 \approx 3.1666666666666665
\][/tex]
2. Express the time as a decimal: The time Harvey takes to run that distance is [tex]\(\frac{1}{4}\)[/tex] hour, which can be directly written as 0.25 hours.
3. Calculate the average speed: The formula for average speed is:
[tex]\[
\text{Average speed} = \frac{\text{Distance}}{\text{Time}}
\][/tex]
Using the values we have:
[tex]\[
\text{Average speed} = \frac{3.1666666666666665 \text{ km}}{0.25 \text{ hours}}
\][/tex]
Performing the division:
[tex]\[
\text{Average speed} = 12.666666666666666 \text{ kilometers per hour}
\][/tex]
Therefore, Harvey's average speed is [tex]\(12.666666666666666\)[/tex] kilometers per hour.
