Let's address this question step-by-step:
1. Equation for Distance:
To determine the distance (d) Jamie will run, we need to use the basic relationship between distance, rate, and time. The formula for distance is given by:
[tex]\[
d = r \times t
\][/tex]
In this formula:
- [tex]\(d\)[/tex] represents the distance in kilometers.
- [tex]\(r\)[/tex] represents the rate in kilometers per hour.
- [tex]\(t\)[/tex] represents the time in hours.
Jamie plans to run for [tex]\(\frac{1}{2}\)[/tex] of an hour, so we can substitute [tex]\(t = \frac{1}{2}\)[/tex] into the equation:
[tex]\[
d = r \times \frac{1}{2}
\][/tex]
2. Calculating the Distance at a Given Rate:
Next, we are asked to find out how far Jamie will run if they choose a rate of 8 kilometers per hour. We need to substitute [tex]\(r = 8\)[/tex] into the equation we have:
[tex]\[
d = 8 \times \frac{1}{2}
\][/tex]
Multiplying the values:
[tex]\[
d = 8 \times 0.5
\][/tex]
[tex]\[
d = 4
\][/tex]
Thus, if Jamie runs at a rate of 8 kilometers per hour, they will cover a distance of [tex]\( \boxed{4} \)[/tex] kilometers in [tex]\(\frac{1}{2}\)[/tex] of an hour.
