Problem:
In an -meter race, Sunny is exactly meters ahead of Windy when Sunny finishes the race. The next time they race, Sunny sportingly starts meters behind Windy, who is at the starting line. Both runners run at the same constant speed as they did in the first race. How many meters ahead is Sunny when Sunny finishes the second race?
Answer Choices:
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Solution:
Let be Sunny's rate. Thus and are the times it takes Sunny to cover meters and meters, respectively. Because Windy covers only meters while Sunny is covering meters, it follows that Windy's rate is . While Sunny runs meters, the number of meters Windy runs is . Sunny's victory margin over Windy is .