To determine Maura's distance south of Chicago, we need to use the given relationship between the number of hours [tex]\( h \)[/tex] she has driven and the total distance [tex]\( k \)[/tex] she is south of Chicago. We start by recalling that Maura was initially 73 kilometers south of Chicago and she continues driving further south at a speed of 72 kilometers per hour.
The formula to calculate the total distance [tex]\( k \)[/tex] she is south of Chicago after [tex]\( h \)[/tex] hours is:
[tex]\[ k = 73 + 72h \][/tex]
Let's calculate [tex]\( k \)[/tex] for each value of [tex]\( h \)[/tex] given in the table:
1. When [tex]\( h = 2 \)[/tex]:
[tex]\[
k = 73 + 72 \times 2
\][/tex]
[tex]\[
k = 73 + 144
\][/tex]
[tex]\[
k = 217
\][/tex]
2. When [tex]\( h = 4 \)[/tex]:
[tex]\[
k = 73 + 72 \times 4
\][/tex]
[tex]\[
k = 73 + 288
\][/tex]
[tex]\[
k = 361
\][/tex]
3. When [tex]\( h = 6 \)[/tex]:
[tex]\[
k = 73 + 72 \times 6
\][/tex]
[tex]\[
k = 73 + 432
\][/tex]
[tex]\[
k = 505
\][/tex]
4. When [tex]\( h = 8 \)[/tex]:
[tex]\[
k = 73 + 72 \times 8
\][/tex]
[tex]\[
k = 73 + 576
\][/tex]
[tex]\[
k = 649
\][/tex]
Now we can complete the table:
[tex]\[
\begin{tabular}{|c|c|}
\hline
$h$ & $k$ \\
\hline
2 & 217 \\
\hline
4 & 361 \\
\hline
6 & 505 \\
\hline
8 & 649 \\
\hline
\end{tabular}
\][/tex]
