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?

The correct option is 60-inch, South.

To determine the distance and direction of the Parking Lot model with respect to the Science Lab model, let us plot the positions of each facility step-by-step using Cartesian coordinates (East/West as the X-axis, North/South as the Y-axis).

Step 1: Set a reference point for the Admin Building model.
Let the coordinates of the Admin Building model be $(0,0)$.

Step 2: Find the position of the Science Lab model.
The Admin Building model is 50 inches to the west of the Science Lab model.
This means the Science Lab model is 50 inches to the east of the Admin Building model.
Coordinates of Science Lab model = $(50,0)$.

Step 3: Find the position of the Sports Center model.
The Science Lab model is 40 inches to the north of the Sports Center model.
This means the Sports Center model is 40 inches to the south of the Science Lab model.
Coordinates of Sports Center model = $(50,-40)$.

Step 4: Find the position of the Hostel model.
The Hostel model is 30 inches to the west of the Sports Center model.
X-coordinate of Hostel model = $50-30=20$.
Coordinates of Hostel model = $(20,-40)$.

Step 5: Find the position of the Dining Hall model.
The Hostel model is 20 inches to the north of the Dining Hall model.
This means the Dining Hall model is 20 inches to the south of the Hostel model.
Y-coordinate of Dining Hall model = $-40-20=-60$.
Coordinates of Dining Hall model = $(20,-60)$.

Step 6: Find the position of the Parking Lot model.
The Dining Hall model is 30 inches to the west of the Parking Lot model.
This means the Parking Lot model is 30 inches to the east of the Dining Hall model.
X-coordinate of Parking Lot model = $20+30=50$.
Coordinates of Parking Lot model = $(50,-60)$.

Step 7: Determine the relative position of the Parking Lot model with respect to the Science Lab model.
Coordinates of Science Lab model = $(50,0)$.
Coordinates of Parking Lot model = $(50,-60)$.

Both models have the same X-coordinate ($50$ inches East).
Difference in Y-coordinates = $0-(-60)=60$ inches.

Since the Y-coordinate of the Parking Lot model is lower ($-60$), it is located directly to the South of the Science Lab model.

Therefore, the Parking Lot model is 60-inch, South with respect to the Science Lab model.