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 of the runners are proportional, we need to calculate the speeds as distance divided by time:
Liam: 0.5 miles / 306.6 seconds = 0.00163 miles per second
Taylor: 1.2 miles / 756.36 seconds = 0.00158 miles per second
Sarah: 0.7 miles / 504.35 seconds = 0.00139 miles per second
Ashley: 0.75 miles / 459.9 seconds = 0.00163 miles per second
Connor: 1 mile / 600.5 seconds = 0.00166 miles per second
Nathan: 1.5 miles / 942.75 seconds = 0.00159 miles per second
Juan: 1.35 miles / 827.82 seconds = 0.00163 miles per second
Katie: 0.6 miles / 429.48 seconds = 0.00140 miles per second
Based on the calculations, the speeds of Liam, Ashley, and Juan are in a proportional relationship because they have the same value of 0.00163 miles per second.