During the Labor Day weekend, Amy and Kathleen each ran in a race. Amy ran in a 5K and completed it in 31 minutes and 15 seconds. Kathleen ran in a half-marathon, which is 21.1 kilometers, and completed it in 2 hours, 11 minutes, and 52.5 seconds.
Let d represent distance in kilometers, r represent the rate, and t represent time in minutes. The proportional relationship d = r * t can be used to determine the speed at which Amy and Kathleen ran their respective races. Using Amy's distance and time, the proportional relationship 5 = r * 31.25 can be used to determine her rate. Using Kathleen's distance and time, the proportional relationship 21.1 = r * 131.88 can be used to determine her rate. Based on the actual rates that they ran during their respective races, Amy ran at the same rate as Kathleen.
(Note: 31 minutes and 15 seconds is equivalent to 31.25 minutes, and 2 hours, 11 minutes, and 52.5 seconds is equivalent to 131.88 minutes.)
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