Explanation:

To find the ratio of the time taken by the cars to travel the same distance, we need to understand the relationship between speed, distance, and time.

- Speed and Time Relationship: Time is inversely proportional to speed when the distance is constant. This means if one car is faster, it takes less time to cover the same distance.

- Given Speed Ratio: 3:4:8. This means if the first car's speed is 3 units, the second's is 4 units, and the third's is 8 units.

- Time Ratio Calculation:

- For the first car: \( \text{Time} \propto \frac{1}{\text{Speed}} = \frac{1}{3} \)

- For the second car: \( \text{Time} \propto \frac{1}{4} \)

- For the third car: \( \text{Time} \propto \frac{1}{8} \)

- Time Ratio: Inverting the speed ratio 3:4:8 gives you 1/3 : 1/4 : 1/8. To compare these, find a common factor and invert:

- Convert to whole numbers: Multiply by the least common multiple of 3, 4, and 8, which is 24.

- \( \frac{1}{3} \times 24 = 8 \)

- \( \frac{1}{4} \times 24 = 6 \)

- \( \frac{1}{8} \times 24 = 3 \)

- Final Ratio of Times: 8:6:3

- Correct Option: \(\underline{\color{green}{\text{8:6:3}}}\)