Explanation:

To determine the total distance, consider these points:

- The total journey time is 1 hour and 24 minutes, which is 1.4 hours.

- Let's assume the total distance is D km.

- The car covers two-thirds of the distance at 52 km/h.

- This portion would be (2/3)D.

- Time taken for this portion = (2/3)D / 52 hours.

- The rest of the distance is one-third, covered at 65 km/h.

- This portion would be (1/3)D.

- Time taken for this portion = (1/3)D / 65 hours.

- Total time taken = Time for first part + Time for second part = 1.4 hours.

- Using the above information, solve the equation:

$$

\frac{2D}{3 \times 52} + \frac{D}{3 \times 65} = 1.4

$$

- Simplify and solve for D.

After computation, the correct answer is:

- Option 1: 78 km