Average speed over a multi-leg trip with different speeds: Columbus travels 200 km from Lucknow to Kolkata at 40 km/h, then 300 km to Bengaluru at 20 km/h, and finally 500 km to Ahmedabad at 10 km/h. What is his overall average speed for the full 1000 km journey?

Introduction / Context:
Average speed for a complete trip equals total distance divided by total time, not the average of speeds. When each leg covers a fixed distance at a different speed, we must compute each leg’s time and sum them.

Given Data / Assumptions:

• D1 = 200 km at v1 = 40 km/h
• D2 = 300 km at v2 = 20 km/h
• D3 = 500 km at v3 = 10 km/h
• Total distance D = 1000 km

Concept / Approach:
Total time T = D1/v1 + D2/v2 + D3/v3. Overall average speed v_avg = D / T. Avoid taking a naive mean of 40, 20, and 10 because distances differ and time is the true averaging weight.

Step-by-Step Solution:
T1 = 200 / 40 = 5 hT2 = 300 / 20 = 15 hT3 = 500 / 10 = 50 hTotal T = 5 + 15 + 50 = 70 hv_avg = 1000 / 70 = 14.2857… km/h = 14 2/7 km/h

Verification / Alternative check:
Because the slowest leg (10 km/h) covers the largest distance, the average must be closer to 10 than to 20 or 40; 14 2/7 fits this intuition.

Why Other Options Are Wrong:
14 5/7 and 15.6 km/h are too high; “none of these” is incorrect because 14 2/7 exactly matches the computed value; 13 6/7 is too low.

Common Pitfalls:
Averaging speeds arithmetically or weighting by distances incorrectly. Always compute total time explicitly.

Final Answer:
14 2/7 KM/hr