A man complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km.

Step 1: Let's denote the total distance of the journey as D. We know that the man travels the first half of the journey (D/2) at a speed of 21 km/hr and the second half of the journey (D/2) at a speed of 24 km/hr.

Step 2: We know that time is equal to distance divided by speed. So, the time taken to travel the first half of the journey is (D/2)/21 and the time taken to travel the second half of the journey is (D/2)/24.

Step 3: The total time taken for the journey is the sum of the time taken for the first half and the second half. We know that the total time taken is 10 hours. So, we can set up the equation: (D/2)/21 + (D/2)/24 = 10.

Step 4: To solve for D, we first need to get rid of the fractions. Multiply all terms by the least common multiple of 21 and 24, which is 504. This gives us: 12D + 10.5D = 5040.

Step 5: Combine like terms to get: 22.5D = 5040.

Step 6: Finally, solve for D by dividing both sides of the equation by 22.5. This gives us: D = 5040 / 22.5 = 224 km.

So, the total distance of the journey is 224 km.