Answer:
[tex]\begin{gathered} A.d=\frac{13}{14}t+0 \\ B\text{. 6:42 P.M.} \end{gathered}[/tex]Explanation:
The distance between Grand Rapids and Lansing = 65 miles
The time taken between Grand Rapids and Lansing ( 4:00 P.M. to 5:10 P.M. ) = 1 hour 10 minutes
= 70 minutes
The speed at which you are driving is:
[tex]\begin{gathered} s=\frac{d}{t} \\ s=65\div70 \\ s=\frac{13}{14}\text{ miles per minute} \end{gathered}[/tex]Thus, a linear equation that gives the distance in terms of t is:
[tex]\begin{gathered} \frac{13}{14}=\frac{d}{t} \\ d=\frac{13}{14}t \end{gathered}[/tex]Part B
If Detroit is 150 miles from Grand Rapids:
d=150 miles
[tex]\begin{gathered} d=\frac{13}{14}t \\ 150=\frac{13}{14}t \\ t=150\times\frac{14}{13} \\ t\approx162\text{ minutes} \\ 162\text{ minutes = 2 hours 42 minutes} \end{gathered}[/tex]So, the time from Grand Rapids to Detroit is 2 hours 42 minutes.
Therefore, if you leave Grand Rapids at 4:00 P.M., you will arrive in Detroit at approximately 6:42 P.M.