Step 1 :Let's denote the time Maria took to drive to the appointment as \(t\) hours. Therefore, the time she took to return is \(t + 0.5\) hours.
Step 2 :We know that the distance is the same for both trips, and distance is calculated as speed multiplied by time. Therefore, we can set up the following equation: \(30t = 20(t + 0.5)\).
Step 3 :Solving this equation gives us \(t = 1\) hour. This is the time Maria took to drive to the appointment.
Step 4 :Now, we can calculate the distance Maria traveled to the appointment. Using the formula for distance (speed multiplied by time), we get \(30 \times 1 = 30\) miles.
Step 5 :Final Answer: The distance Maria traveled to the appointment is \(\boxed{30}\) miles.