In the morning, Maria drove to a business appointment at $30 \mathrm{mph}$. Her average speed on the return trip in the afternoon was $20 \mathrm{mph}$. The return trip took $\frac{1}{2} \mathrm{hr}$ longer because of heavy traffic. How far did she travel to the appointment?

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.