Miguel has driven \( \frac{2}{3} \) of the total distance in 4 hours. To find the total time, we can set up the problem as follows:
Let the total distance be represented as \( D \) and the total time be represented as \( T \).
If Miguel has driven \( \frac{2}{3}D \) in 4 hours, we can find the rate of driving: \[ \text{Rate} = \frac{\text{Distance}}{\text{Time}} = \frac{\frac{2}{3}D}{4} = \frac{2D}{12} = \frac{D}{6} \]
Now, if \( T \) is the total time to drive the entire distance \( D \), then the rate can also be expressed as: \[ \text{Rate} = \frac{D}{T} \]
Since both expressions represent the same rate, we set them equal: \[ \frac{D}{T} = \frac{D}{6} \]
Assuming \( D \) is not zero (as distance cannot be zero), we can simplify: \[ \frac{1}{T} = \frac{1}{6} \]
From this, we solve for \( T \): \[ T = 6 \text{ hours} \]
Now, because Miguel has already driven for 4 hours to cover \( \frac{2}{3}D \), he has \( \frac{1}{3}D \) left to drive. To find the time it takes to drive the remaining distance, we use the rate: \[ \text{Time for the remaining } \frac{1}{3}D = \text{Distance} \div \text{Rate} = \frac{\frac{1}{3}D}{\frac{D}{6}} = \frac{1}{3}D \times \frac{6}{D} = 2 \text{ hours} \]
So, the total time for the trip is: \[ 4 \text{ hours} + 2 \text{ hours} = 6 \text{ hours} \]
Thus, the total time it will take Miguel to reach his destination is 6 hours.
1 answer