To find the total time it will take Miguel to reach his destination, we can use ratios and proportions.
We know that Miguel has already driven 2/3 of the total distance and has 4 hours left to drive. Let's assume that the total distance is represented by "x".
The distance Miguel has driven is 2/3 * x.
The remaining distance is 1/3 * x.
We also know that the time it takes to drive a certain distance is directly proportional to the distance. In other words, if it takes Miguel 2/3 of the total time to drive 2/3 of the distance, then it will take him the full total time to drive the full distance.
So, if Miguel has 4 hours left to drive 1/3 of the distance, we can set up the proportion:
2/3 of the distance / 2/3 of the time = 1/3 of the distance / 4 hours
To solve for the total time it will take Miguel to reach his destination, we need to find the value of 1/3 of the time.
Cross-multiplying the proportion:
(2/3 * x) * 4 = (1/3 * x) * (2/3 * x)
8/3 * x = 2/9 * x^2
Now, we can solve the equation for x and find the total time it will take Miguel to reach his destination.
Multiplying both sides by 9:
8/3 * 9 * x = 2/9 * x^2 * 9
24x = 2x^2
Dividing both sides by x:
24 = 2x
Dividing both sides by 2:
12 = x
So, the total distance Miguel needs to travel is 12 units (could be miles or kilometers, depending on the context).
Now, we can substitute the value of x into one of the expressions we derived earlier to find the total time:
Total time = 2/3 of the distance = (2/3) * 12
Total time = 8 hours
Therefore, the total time it will take Miguel to reach his destination is 8 hours.
Thus, the correct answer is A) 8 hours.