A group of friends wanted to compare their average running speeds. They recorded the distance and amount of time each person ran one Saturday morning.
Select all the runners whose speeds are in a proportional relationship with each other.
Name Time (seconds) Distance (miles)
Liam 306.6 0.5
Taylor 756.36 1.2
Sarah 504.35 0.7
Ashley 459.9 0.75
Connor 600.5 1
Nathan 942.75 1.5
Juan 827.82 1.35
Katie 429.48 0.6
To determine if the speeds are in a proportional relationship, we need to compare the ratios of time to distance for each runner.
Liam: 306.6 seconds / 0.5 miles = 613.2 seconds per mile
Taylor: 756.36 seconds / 1.2 miles = 630.3 seconds per mile
Sarah: 504.35 seconds / 0.7 miles = 720.5 seconds per mile
Ashley: 459.9 seconds / 0.75 miles = 613.2 seconds per mile
Connor: 600.5 seconds / 1 mile = 600.5 seconds per mile
Nathan: 942.75 seconds / 1.5 miles = 628.5 seconds per mile
Juan: 827.82 seconds / 1.35 miles = 613.2 seconds per mile
Katie: 429.48 seconds / 0.6 miles = 715.8 seconds per mile
From the ratios, we can see that Liam, Ashley, Connor, and Juan have the same ratio of seconds per mile, indicating a proportional relationship. So, Liam, Ashley, Connor, and Juan have speeds that are in a proportional relationship with each other.