To solve this problem, we can use the formula: time = distance / speed.

Let's assume the distance between Carla's house and her brother's house is D.

When Carla drives to her brother's house at an average speed of 50 miles per hour, the time it takes is given by:
Time = Distance / Speed
Time = D / 50

We are given that Carla takes 3 hours to drive to her brother's house, so we can write the equation:
3 = D / 50

To find the time it takes for Carla to drive home at an average speed of 60 miles per hour, we need to determine the distance between the two locations. Since Carla takes the same route home, the distance remains the same. Thus, D remains constant.

Using the formula for time:
Time = Distance / Speed
Time = D / 60

Now, we need to solve for the value of Time.

Since D / 50 = 3, we can solve for D:
D = 3 * 50
D = 150 miles

Now, substitute the value of D into the formula for the time to drive home:
Time = 150 / 60
Time = 2.5 hours

Therefore, it takes Carla 2.5 hours (or 2 hours and 30 minutes) to drive home.

The answer is (C) 2 hours and 30 minutes.