After a regional sports championship, Tara and Emek reviewed results from several events where athletes had raced over different distances and times. Some competitors appeared faster based only on their finishing times, but the courses were not the same length. They calculated each athlete's unit rate and compared the results carefully, checking whether the original rankings were fair. Their analysis revealed a more accurate leaderboard, and the coaches used the corrected rankings to recognize the strongest overall performances.
Challenges
Challenge 1 of 5
Challenges
Challenge 1 of 4
Hint
Find each athlete's distance per minute before comparing.
Athlete A ran 3.6 km in 12 minutes, and Athlete B ran 4.5 km in 15 minutes. Which statement is correct after comparing their unit rates?
Athlete A was faster.Athlete B was faster.Both athletes had the same unit rate.There is not enough information to compare them.Correct! Both athletes had the same unit rate of 0.3 km per minute.
Try again. Compare the unit rates, not just the distances or times.
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Hint
Convert kilometers to meters first, then divide by the time.
An athlete completed 7.2 kilometers in 24 minutes. What was the athlete's speed in meters per minute?
Correct! The athlete's speed was 300 meters per minute.
Check the unit conversion before dividing by the time.
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Hint
Calculate kilometers per minute for both athletes before judging the ranking.
A coach ranked Athlete X ahead of Athlete Y because X finished in less time. Athlete X ran 2.4 km in 8 minutes, while Athlete Y ran 3.3 km in 11 minutes. What should Tara and Emek conclude after comparing unit rates?
The original ranking was correct because Athlete X had the greater unit rate.The original ranking was incorrect because Athlete Y had the greater unit rate.Both athletes had the same unit rate, so they should be tied.The athletes cannot be compared because they raced different distances.Correct! Both athletes had a unit rate of 0.3 km per minute, so neither was faster.
Remember that finishing time alone is not enough. Compare the unit rates.
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