If X covers 48m while Y covers 42m, by what distance does X defeat Y in a 1km race:_________?
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Answer: B. 125m
Explanation
The problem establishes a constant proportional rate of movement between the two runners over any given distance. Using the given distances, Y covers forty-two meters for every forty-eight meters that X successfully covers. Scaling this ratio to a one-thousand-meter race shows that Y runs eight hundred seventy-five meters, leaving a difference of one hundred twenty-five meters. Race distance problems rely on the assumption of uniform speed to establish direct proportions between competitors. Proportional reasoning allows us to predict outcomes over longer tracks based on small-scale trial measurements. The margin of victory in a running race is calculated as the difference between the total track length and the loser's covered distance.
Option A is incorrect because it results from an arithmetic error in calculating the proportional distance ratio. Option C underestimates the winning margin by using an incorrect multiplier for the secondary runner's pace. Option D is wrong because it fails to maintain the exact fractional relationship between the two distances.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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