Read the following campus layout information carefully and answer the question that follows:

Eight miniature models of university facilities are placed on a display table at various distances from each other. The model of the Admin Building is 50 inches to the west of the Science Lab model. The Library model is 70 inches to the east of the Main Gate model. The Hostel model is 20 inches to the north of the Dining Hall model, which is 30 inches to the west of the Parking Lot model. The Admin Building model is 40 inches to the south of the Main Gate model. The Science Lab model is 40 inches to the north of the Sports Center model. The Hostel model is 30 inches to the west of the Sports Center model.

How far and in which direction is the Parking Lot model with respect to the Science Lab model?

Correct Answer: 60-inch, South

Let us map out the positions of each university facility on a 2D Cartesian coordinate system step-by-step. Let the Admin Building model be at the origin (0, 0).

1. Admin Building:
Position = (0, 0)

2. Science Lab:
The Admin Building is 50 inches to the west of the Science Lab. Therefore, the Science Lab is 50 inches to the east of the Admin Building.
Position = (50, 0)

3. Main Gate:
The Admin Building is 40 inches to the south of the Main Gate. Therefore, the Main Gate is 40 inches to the north of the Admin Building.
Position = (0, 40)

4. Sports Center:
The Science Lab is 40 inches to the north of the Sports Center. Therefore, the Sports Center is 40 inches to the south of the Science Lab.
Position = (50, 0 - 40) = (50, -40)

5. Hostel:
The Hostel is 30 inches to the west of the Sports Center.
Position = (50 - 30, -40) = (20, -40)

6. Dining Hall:
The Hostel is 20 inches to the north of the Dining Hall. Therefore, the Dining Hall is 20 inches to the south of the Hostel.
Position = (20, -40 - 20) = (20, -60)

7. Parking Lot:
The Dining Hall is 30 inches to the west of the Parking Lot. Therefore, the Parking Lot is 30 inches to the east of the Dining Hall.
Position = (20 + 30, -60) = (50, -60)

Now, let us compare the position of the Parking Lot (50, -60) with respect to the Science Lab (50, 0):

Difference in X-coordinates:
$50-50=0$

Difference in Y-coordinates:
$-60-0=-60$

Since the X-coordinates are equal and the Y-coordinate of the Parking Lot is 60 units below (south of) the Science Lab, the Parking Lot model is 60-inch to the South with respect to the Science Lab model.