Let x be the number of miles and y the total cost; therefore, the equations that model the two plans are
[tex]\begin{gathered} PlanA: \\ y_A=30+0.20x \\ PlanB \\ y_B=50 \end{gathered}[/tex]
Then, set y_A=y_B as shown below
[tex]\begin{gathered} y_A=y_B \\ \Rightarrow30+0.20x=50 \\ \Rightarrow0.20x=20 \\ \Rightarrow x=\frac{20}{0.20}=100 \end{gathered}[/tex]
Therefore, once the mileage is greater than 100 miles, the total cost of plan B will be less than that of plan A.
The answer is 100 miles.
