In a 1000 m event, A defeats B by 100 m, whereas in an 800 m event, B defeats C by 100 m. By what margin will A defeat C in a 600 m event?
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Answer: B. 127.5 m
Explanation
A defeats B by one hundred meters in a one thousand meter race, establishing a speed ratio. B defeats C by one hundred meters in an eight hundred meter race, establishing another speed ratio. Combining these proportional speeds and scaling down to six hundred meters yields the exact winning margin. Race proportionalities assume constant running speeds for all participating athletes throughout the entire distance. Ratio scaling allows direct comparison of competitors who never physically raced against each other simultaneously. Calculating distance margins involves finding the exact fractional progress of trailing runners at the finish line.
Proportional reasoning is widely used in sports analytics to rank athletes across different event lengths. Logistics planners use similar scaling techniques to estimate transit times over varying route segments. Mastering relative speed calculations improves problem-solving efficiency in competitive examinations. Option A underestimates the combined proportional speed advantage accumulated by the leading runner over the distance. Option C overshoots the correct proportional distance due to compounding calculation errors in the intermediate steps. Option D relies on incorrect distance reduction factors that distort the true running speed ratios.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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