Answer:
The distance between Shawna's Home and Rochester is 228 mi and takes her 6 hr to make the drive.
Step-by-step explanation:
Known Data
Final distance is the same for both [tex]x_{f}[/tex], but for Terrence [tex]x_{f}-56[/tex], due he didn't arrive for 56 mi
Initial distance is the same for both [tex]x_{i}=0m[/tex]
Shawna's Velocity [tex]v_{S}=38mi/hr[/tex], and time [tex]t[/tex]
Terrence's Velocity [tex]v_{T}=43mi/hr[/tex], and time, as he starts 2hr later [tex]t-2[/tex]
Formula
[tex]x_{f}=x_{i}+vt[/tex], for both cases
Equation System
Shawna: [tex]x_{f}=38t[/tex] or (1) [tex]x-38t=0[/tex]
Terrence: [tex]x_{f}-56=43(t-2)[/tex], [tex]x_{f}-56=43t-86[/tex], [tex]x_{f}-43t=56-86[/tex] and finally (2)[tex]x_{f}-43t=-30[/tex]
By solving this equation system (1) and (2), using any method, we obtain [tex]x_{f}=228\ mi[/tex] and [tex]t=6\ hr[/tex].
