Michael 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 this destination hey 6 hours be 8 hours see 12 hours D 8/3 hours

1 answer

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:

  1. First, find the time per unit distance for \( \frac{2}{3} \): \[ \text{Time per unit distance} = \frac{4 \text{ hours}}{\frac{2}{3}} = 4 \times \frac{3}{2} = 6 \text{ hours} \]

  2. 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.