To determine how many containers the ship can carry at a time, we need to calculate the total available area for containers and then divide it by the area occupied by a single container, taking into account the stacking.

Step 1: Calculate the total area of the ship's deck

The ship's deck is a rectangle, so the total area of the deck is:

$\text{Deck area} = \text{Length} \times \text{Width} = 1,200 \, \text{ft} \times 300 \, \text{ft} = 360,000 \, \text{ft}^2$

Step 2: Calculate the area occupied by one container

Each container is 30 feet long and 10 feet wide, so the area occupied by one container is:

$\text{Container area} = 30 \, \text{ft} \times 10 \, \text{ft} = 300 \, \text{ft}^2$

Step 3: Calculate how many containers fit on the deck (without considering stacking)

To find how many containers can fit on the deck in terms of area, we divide the total deck area by the area of one container:

$\text{Number of containers (area)} = \frac{\text{Deck area}}{\text{Container area}} = \frac{360,000 \, \text{ft}^2}{300 \, \text{ft}^2} = 1,200 \, \text{containers}$

Step 4: Account for the stacking of containers

Since containers can be stacked four high, we multiply the number of containers by 4:

$\text{Total number of containers} = 1,200 \, \text{containers} \times 4 = 4,800 \, \text{containers}$

Final Answer:

The ship can carry 4,800 containers at a time.

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Would you like more details on any of the steps or further explanation?

Related Questions:

1. How would the ship’s capacity change if containers could only be stacked two high?
2. What would happen if the ship's length or width was increased by 10%?
3. How much space would 4,800 containers take if stacked in a 3D grid instead of a 2D arrangement?
4. If containers were rearranged to optimize space, how could the deck layout change?
5. What is the total volume occupied by 4,800 containers on the deck?

Tip: Always check if there are any constraints on the ship's layout that may prevent containers from being stacked in a perfect grid.