To find the total time it will take Miguel to reach his destination, we first establish the relationship between the distance he has traveled and the total distance.
Miguel has driven \( \frac{2}{3} \) of the total distance in 4 hours. This means that:
- The distance he has left to drive is \( 1 - \frac{2}{3} = \frac{1}{3} \) of the total distance.
Since he has driven \( \frac{2}{3} \) of the distance in 4 hours, we can find the rate at which he is driving. The time taken for \( \frac{2}{3} \) of the distance is 4 hours, so the time to drive the full distance can be calculated as follows:
- Let \( T \) be the total time to drive the complete distance.
- The relationship can be expressed as: \[ \frac{2}{3} \text{ of distance} \Rightarrow 4 \text{ hours} \] \[ \frac{1}{3} \text{ of distance} \Rightarrow \text{ (let's find this time)} \]
Since \( \frac{2}{3} \) of the total distance takes 4 hours, the time required for \( \frac{1}{3} \) of the distance can be calculated as follows:
The time it takes to travel full distance can be calculated:
Using the ratios: \[ \text{If } \frac{2}{3} \text{ takes } 4 \text{ hours, then } \frac{1}{3} \text{ would take } \frac{4 \text{ hours}}{2} = 2 \text{ hours}. \]
Therefore, the total time \( T \) to complete the total distance is: \[ T = 4 \text{ hours} + 2 \text{ hours} = 6 \text{ hours}. \]
So, the total time it will take Miguel to reach his destination is \( \boxed{6} \) hours.
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