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.

Question

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.

Answer 1

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.

Answer 2

simplify it

Answer 3

Amy and Kathleen both ran at a rate of 0.16 km/min during their respective races.