GATE 2025 AR — Planning – Question 63

Urban Land Use and Transportation · Traffic survey methods, Traffic flow Analysis · 2 marks · Numerical answer

Eight spot speeds are 42, 52, 56, X, 53, 62, 65, 48 km/hour. Time-mean speed is 56.25 km/hour. Determine X and give space-mean speed in km/hour, to two decimals.

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Correct answer: 52.00 to 57.00

Explanation

Time-mean speed is the arithmetic mean. The total of eight speeds is 8×56.25=450 km/hour; the seven known values sum 378, so X=72. Space-mean speed for equal-distance observations is the harmonic mean. The reciprocal sum is approximately 0.14600123, hence $v_s=8/0.14600123=54.79406$ km/hour, or 54.79. Different speeds make this smaller than the arithmetic mean.

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