Let's solve the problem step-by-step to find out the distance from Jorden's home to the store and fill out the table accordingly.
1. Identify the Given Data:
- Rate to store: [tex]\( 30 \)[/tex] miles per hour.
- Rate returning home: [tex]\( 20 \)[/tex] miles per hour.
- Total driving time: [tex]\( 0.5 \)[/tex] hours (30 minutes).
2. Setting Up the Problem:
- Let [tex]\( d \)[/tex] be the distance to the store (in miles).
3. Time Calculation:
- Time to store = [tex]\( \frac{d}{30} \)[/tex] hours.
- Time returning home = [tex]\( \frac{d}{20} \)[/tex] hours.
- Total time = Time to store + Time returning home = [tex]\( 0.5 \)[/tex] hours.
4. Formulating the Equation:
- [tex]\( \frac{d}{30} + \frac{d}{20} = 0.5 \)[/tex]
5. Find the Distance:
- Solving the equation for [tex]\( d \)[/tex]:
[tex]\[ \frac{d}{30} + \frac{d}{20} = 0.5 \][/tex]
To solve for [tex]\( d \)[/tex], find a common denominator (60) and solve:
[tex]\[ \frac{2d}{60} + \frac{3d}{60} = 0.5 \][/tex]
[tex]\[ \frac{5d}{60} = 0.5 \][/tex]
[tex]\[ \frac{d}{12} = 0.5 \][/tex]
[tex]\[ d = 0.5 \times 12 \][/tex]
[tex]\[ d = 6 \][/tex]
Thus, the distance from Jorden’s home to the store is 6 miles.
6. Fill Out the Table:
- The rate heading to the store is [tex]\( 30 \)[/tex] mph.
- The rate returning home is [tex]\( 20 \)[/tex] mph.
- Distance to the store (c) is [tex]\( 6 \)[/tex] miles.
- Distance returning home (d) is [tex]\( 6 \)[/tex] miles.
- Time heading to the store = [tex]\( \frac{6}{30} = 0.2 \)[/tex] hours.
- Time returning home = [tex]\( \frac{6}{20} = 0.3 \)[/tex] hours.
[tex]\[
\begin{array}{|c|c|c|c|}
\hline \multicolumn{2}{|c|}{\text{Distance}} & \text{Rate} & \text{Time} \\
\hline \text{To store} & 6 & 30 & 0.2 \\
\hline \text{Return} \text{home} & 6 & 20 & 0.3 \\
\hline
\end{array}
\][/tex]
This completes the solution and fills out the table correctly.
