A car covers four successive stretches of 3 km each at speeds of 10 km/h, 20 km/h, 30 km/h, and 60 km/h, respectively. What is the average speed over the entire 12 km journey?
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A10 km/h
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B20 km/h
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C30 km/h
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D25 km/h
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E24 km/h
Answer
Correct Answer: 20 km/h
Explanation
Introduction / Context:When equal distances are traveled at different speeds, the average speed is found from total distance divided by total time—effectively a harmonic-mean type across the segments.
Given Data / Assumptions:
- Four segments, each 3 km (total 12 km).
- Speeds: 10, 20, 30, 60 km/h.
Concept / Approach:Total time equals the sum of segment times d/vi. Average speed = total distance / total time.
Step-by-Step Solution:
Times: 3/10 + 3/20 + 3/30 + 3/60 hours= 0.3 + 0.15 + 0.1 + 0.05 = 0.6 hoursAverage speed = 12 km / 0.6 h = 20 km/hVerification / Alternative check:Harmonic-mean style: V = 4 / (1/10 + 1/20 + 1/30 + 1/60) = 20.
Why Other Options Are Wrong:Arithmetic means (like 30 km/h) do not account for the longer time spent at slower speeds; 25 or 24 km/h are near-miss distractors.
Common Pitfalls:Averaging the speeds directly instead of using time-weighted averaging via total time.
Final Answer:20 km/h