Answer:
The relationship is rate is same.
Step-by-step explanation:
Given : 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.
To find : The proportional relationship ?
Solution :
We know, [tex]r=\frac{d}{t}[/tex]
1 hour = 60 minutes = 60 × 60 seconds
First we find the rate of both Amy and Kathleen.
Amy ran in a 5 km and completed it in 31 minutes and 15 seconds.
Rate of Amy in km/hr is given by,
[tex]r_1=\frac{5}{\frac{31}{60}+\frac{15}{60\times 60}}[/tex]
[tex]r_1=\frac{5}{0.516+0.00416}[/tex]
[tex]r_1=\frac{5}{0.52016}[/tex]
[tex]r_1=9.6km/hr[/tex]
Kathleen ran in a half-marathon, which is 21.1 kilometers, and completed it in 2 hours, 11 minutes, and 52.5 seconds.
Rate of Kathleen in km/hr is given by,
[tex]r_2=\frac{21.1}{2+\frac{11}{60}+\frac{52.5}{60\times 60}}[/tex]
[tex]r_2=\frac{5}{2+0.18333+0.014583}[/tex]
[tex]r_2=\frac{5}{2.197}[/tex]
[tex]r_2=9.6km/hr[/tex]
Both man ran at the same speed.
Therefore, The relationship is rate is same.
