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
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
can be used to determine her rate. Using Kathleen's distance and time, the proportional relationship
can be used to determine her rate. Based on the actual rates that they ran during their respective races, Amy ran at
Kathleen.
To find Amy's rate, we need to convert her time to minutes and her distance to kilometers.
Amy's time in minutes = 31 + 15/60 = 31.25 minutes
Amy's distance in kilometers = 5
Amy's rate = distance / time = 5 / 31.25 = 0.16 km/min
To find Kathleen's rate, we need to convert her time to minutes and her distance to kilometers.
Kathleen's time in minutes = 2 * 60 + 11 + 52.5/60 = 131.875 minutes
Kathleen's distance in kilometers = 21.1
Kathleen's rate = distance / time = 21.1 / 131.875 = 0.16 km/min
Therefore, Amy and Kathleen ran at the same rate during their respective races.
simplify it
Amy and Kathleen both ran at a rate of 0.16 km/min during their respective races.
To determine the rates at which Amy and Kathleen ran their races, we can use the proportional relationship equation: r = d/t, where r represents the rate, d represents the distance, and t represents the time.
First, let's calculate Amy's rate. Amy ran a 5K race, which is equal to 5 kilometers, and she completed it in 31 minutes and 15 seconds. To convert the time into minutes, we can calculate it as follows: 31 minutes + 15 seconds/60 (since there are 60 seconds in a minute) = 31.25 minutes.
Now we can use the proportion: r = d/t. Plugging in the values for Amy, we get r = 5 km / 31.25 minutes ≈ 0.16 km/minute.
Next, let's calculate Kathleen's rate. Kathleen ran a half-marathon, which is equal to 21.1 kilometers, and she completed it in 2 hours, 11 minutes, and 52.5 seconds. To convert the time into minutes, we can calculate it as follows: 2 hours × 60 minutes + 11 minutes + 52.5 seconds/60 = 131.875 minutes (rounded to three decimal places).
Using the proportion: r = d/t, we can plug in the values for Kathleen: r = 21.1 km / 131.875 minutes ≈ 0.16 km/minute (rounded to two decimal places).
Therefore, both Amy and Kathleen ran at a rate of approximately 0.16 km/minute during their respective races.