First, we need to find the rate at which the oil spill spreads. The oil spill covers 4 square kilometers in \( \frac{1}{4} \) of an hour.
To find the rate, we calculate:
\[ \text{Rate} = \frac{\text{Area}}{\text{Time}} = \frac{4 \text{ km}^2}{\frac{1}{4} \text{ hour}} = 4 \text{ km}^2 \times 4 = 16 \text{ km}^2/\text{hour} \]
Now that we have the rate of 16 square kilometers per hour, we can calculate how much area it will cover in 2 hours:
\[ \text{Area in 2 hours} = \text{Rate} \times \text{Time} = 16 \text{ km}^2/\text{hour} \times 2 \text{ hours} = 32 \text{ km}^2 \]
Thus, the oil spill will cover 32 square kilometers in 2 hours.
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