Average speed with distance fractions at different speeds: Mr. Bundda covers 1/4 of the journey at 8 km/h, 3/5 at 6 km/h, and the remaining 3/20 at 10 km/h. What is his average speed for the whole trip?

Introduction / Context:When speeds apply to fractions of distance, average speed is computed from the reciprocal-time sum: 1/v_avg = Σ(fi / vi), where fi are distance fractions and vi are the corresponding speeds.

Given Data / Assumptions:

• Fractions: 1/4, 3/5, 3/20 (sum = 1)
• Speeds: 8 km/h, 6 km/h, 10 km/h respectively

Concept / Approach:Compute 1/v_avg = (1/4)/8 + (3/5)/6 + (3/20)/10 and invert to get v_avg.

Step-by-Step Solution:(1/4)/8 = 1/32 = 0.03125(3/5)/6 = 3/30 = 0.1(3/20)/10 = 3/200 = 0.015Sum = 0.03125 + 0.1 + 0.015 = 0.14625v_avg = 1 / 0.14625 ≈ 6.834 km/h

Verification / Alternative check:Let total distance be 1 unit; compute times 0.25/8, 0.6/6, 0.15/10, sum them, then v_avg = 1 / total time. The result matches 6.83 km/h.

Why Other Options Are Wrong:9 and 8.5 are too high; 4 is too low; 7.2 does not equal the computed harmonic-like combination.

Common Pitfalls:Treating the average as an arithmetic mean of speeds or weighting by time incorrectly when the fractions refer to distance portions.

Final Answer:6.83 km/h