Michael has driven \( \frac{2}{3} \) of the total distance in 4 hours. Since he has completed \( \frac{2}{3} \) of the distance, the remaining distance is \( \frac{1}{3} \).
To find out how long it will take him to drive the remaining \( \frac{1}{3} \) of the distance at the same rate, we can set up a proportion.
If \( \frac{2}{3} \) of the distance takes 4 hours, then:
\[ \text{Time to drive } \frac{1}{3} \text{ of the distance} = \left(\frac{4 \text{ hours}}{\frac{2}{3}}\right) \times \frac{1}{3} \]
Calculating that:
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First, find the time per unit distance for \( \frac{2}{3} \): \[ \text{Time per unit distance} = \frac{4 \text{ hours}}{\frac{2}{3}} = 4 \times \frac{3}{2} = 6 \text{ hours} \]
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Now calculate the time for \( \frac{1}{3} \): \[ \text{Time to drive } \frac{1}{3} \text{ of the distance} = 6 \text{ hours} \times \frac{1}{3} = 2 \text{ hours} \]
Now, the total time to complete the entire trip will be the time already spent (4 hours) plus the time to cover the remaining distance (2 hours):
\[ \text{Total time} = 4 \text{ hours} + 2 \text{ hours} = 6 \text{ hours} \]
Thus, the total time it will take him to reach his destination is 6 hours.
So the answer is option A: 6 hours.