A car completes a certain journey in 8 hours. It covers half the distance at 40 km/hr. and the rest at 60 km/hr. The length of the journey is—Select one:a. 420 kmb. 400 kmc. 384 kmd. 350 km

To solve this problem, we need to find the total distance covered by the car. We know that the car travels half the distance at 40 km/hr and the other half at 60 km/hr.

Step 1: Calculate the time taken to cover each half of the journey.

For the first half of the journey at 40 km/hr, we don't know the distance yet, but we know that it's half of the total distance. Let's denote the total distance as D. So, the distance for the first half of the journey is D/2.

We know that time = distance/speed. Therefore, the time taken for the first half of the journey is (D/2) / 40.

For the second half of the journey at 60 km/hr, the distance is also D/2. So, the time taken for the second half of the journey is (D/2) / 60.

Step 2: Add the times together.

We know that the total time for the journey is 8 hours. So, we can set up the equation:

(D/2) / 40 + (D/2) / 60 = 8

Step 3: Solve for D.

To make the equation easier to solve, we can multiply every term by 240 (which is the least common multiple of 40 and 60):

3D + 4D = 1920

This simplifies to:

7D = 1920

Finally, solve for D by dividing both sides by 7:

D = 1920 / 7 = 274.2857 km

However, this is not one of the options given. It seems there might be a mistake in the problem or the answer choices.