Average speed over multiple legs with given distances and speeds: A person travels 9 km at 3 km/h, 25 km at 5 km/h, and 30 km at 10 km/h. What is the overall average speed (in km/h)?

Introduction / Context:
Overall average speed equals total distance divided by total time across all legs. Distances are not equal, so do not use a simple mean of the speeds.

Given Data / Assumptions:

• D1 = 9 km at 3 km/h
• D2 = 25 km at 5 km/h
• D3 = 30 km at 10 km/h

Concept / Approach:
Compute times for each leg, sum them, then divide total distance by total time: v_avg = (D1 + D2 + D3) / (D1/v1 + D2/v2 + D3/v3).

Step-by-Step Solution:
Total distance = 9 + 25 + 30 = 64 kmTotal time = 9/3 + 25/5 + 30/10 = 3 + 5 + 3 = 11 hv_avg = 64 / 11 km/h

Verification / Alternative check:
64/11 ≈ 5.818 km/h, which lies between the minimum and maximum speeds and is weighted toward longer, slower legs.

Why Other Options Are Wrong:
59/11, 115/9, 95/11, and 55/11 do not match total distance divided by total time here.

Common Pitfalls:
Averaging speeds arithmetically or miscomputing time on each leg. Always convert to times before combining.

Final Answer:
64/11 km/h