Sharad completes his journey in 11 hours. He covers half the distance of the…

For a journey split into two equal-distance legs travelled at speeds v1 and v2, total time = (half-distance ÷ v1) + (half-distance ÷ v2). Equivalently, the average speed for such a journey is the harmonic mean 2·v1·v2/(v1+v2), and total distance = average speed × total time.

Applying this to Sharad's journey:

1. Let the total distance of the journey be D km, so each half of the journey is D/2 km.

2. Time taken on the first half at 20 km/hr = (D/2) ÷ 20 = D/40 hours.

3. Time taken on the second half at 30 km/hr = (D/2) ÷ 30 = D/60 hours.

4. Total time = D/40 + D/60 = (3D + 2D)/120 = 5D/120 = D/24 hours.

5. The question states the total journey takes 11 hours, so D/24 = 11.

6. Solving for D: D = 11 × 24 = 264 km.

Cross-check using the average-speed formula: average speed = (2 × 20 × 30)/(20 + 30) = 1200/50 = 24 km/hr, and distance = average speed × time = 24 × 11 = 264 km, which matches. Direct verification: half of 264 km is 132 km; 132 ÷ 20 = 6.6 hours and 132 ÷ 30 = 4.4 hours, and 6.6 + 4.4 = 11 hours, exactly as given.

Hence, the distance of the journey is 264 km.