To fill in the blanks based on the information provided:
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Let d represent distance in kilometers, r represent the rate, and t represent time in minutes.
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The proportional relationship d = r * t can be used to determine the speed at which Amy and Kathleen ran their respective races.
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Using Amy's distance and time, the proportional relationship r = d / t can be used to determine her rate.
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Using Kathleen's distance and time, the proportional relationship r = d / t can be used to determine her rate.
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Based on the actual rates that they ran during their respective races, Amy ran at a slower pace than Kathleen.
To compute the rates, we first need to convert all times to minutes:
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Amy's Rate:
- Distance: 5K = 5 kilometers
- Time: 31 minutes and 15 seconds = 31.25 minutes (31 + 15/60)
\( r_A = \frac{d_A}{t_A} = \frac{5}{31.25} \approx 0.16 \text{ km/min} \)
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Kathleen's Rate:
- Distance: Half-marathon = 21.1 kilometers
- Time: 2 hours, 11 minutes, and 52.5 seconds = 131.875 minutes (2 \times 60 + 11 + 52.5/60)
\( r_K = \frac{d_K}{t_K} = \frac{21.1}{131.875} \approx 0.16 \text{ km/min} \)
Thus, we can see that Amy and Kathleen ran at similar rates with Kathleen's rate slightly lower, thereby confirming that Amy ran at a faster pace than Kathleen.
Therefore, consider this when stating that Amy ran at a faster pace than Kathleen.
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