Problem: In a ten-mile race First beats Second by miles and First beats Third by miles. If the runners maintain constant speeds throughout the race, by how many miles does Second beat Third?
Answer Choices:
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Solution:
From the given information the ratio of the distances covered by First, Second, and Third, in that order, is . Since the speeds remain constant the ratio of the distances remains constant, that, when Second completes an additional miles. Third completes an additional miles since where is the additional distance completed by Third. Therefore, when Second completes miles. Third completes miles, that is, Second beats Third by miles.