Miguel is returning from a trip. In 4 hours, he has driven 2/3 of the total distance. He wants to know how long the total drive will take. At this rate, what is the total time it will take him to reach his destination?(1 point)

Responses

8 hours
8 hours

12 hours
12 hours

6 hours
6 hours

8/3 hours

1 answer

Miguel has driven \( \frac{2}{3} \) of the total distance in 4 hours. To find the total time for the entire trip, we can set up a proportion.

Let \( T \) represent the total time for the trip. The distance he has left to drive is \( \frac{1}{3} \) of the total distance.

Since he has driven \( \frac{2}{3} \) of the distance in 4 hours, we can find the time it will take to drive the remaining \( \frac{1}{3} \) of the distance:

\[ \text{Time to drive } \frac{2}{3} \text{ of the distance} = 4 \text{ hours} \]

To find the time to drive the remaining \( \frac{1}{3} \) of the distance, we can use the ratio of the distances:

If \( \frac{2}{3} \) takes 4 hours, then \( \frac{1}{3} \) would take:

\[ \text{Time for } \frac{1}{3} = 4 \text{ hours} \times \frac{1/3}{2/3} = 4 \text{ hours} \times \frac{1}{2} = 2 \text{ hours} \]

Therefore, the total time \( T \) to reach his destination is:

\[ T = 4 \text{ hours} + 2 \text{ hours} = 6 \text{ hours} \]

So the correct response is:

6 hours