Select the correct text in the table and pick ONE student

Question

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

Answer 1

To determine which runners have speeds that are in a proportional relationship with each other, we need to calculate the speed (miles per second) for each runner by dividing the distance by the time.

Here are the calculations for each runner:

1. Liam:

   • Speed = Distance / Time = 0.5 miles / 306.6 seconds ≈ 0.00163 miles/second

2. Taylor:

   • Speed = 1.2 miles / 756.36 seconds ≈ 0.00159 miles/second

3. Sarah:

   • Speed = 0.7 miles / 504.35 seconds ≈ 0.00139 miles/second

4. Ashley:

   • Speed = 0.75 miles / 459.9 seconds ≈ 0.00163 miles/second

5. Connor:

   • Speed = 1 mile / 600.5 seconds ≈ 0.00166 miles/second

6. Nathan:

   • Speed = 1.5 miles / 942.75 seconds ≈ 0.00159 miles/second

7. Juan:

   • Speed = 1.35 miles / 827.82 seconds ≈ 0.00163 miles/second

8. Katie:

   • Speed = 0.6 miles / 429.48 seconds ≈ 0.00140 miles/second

Next, let's look for groups of runners with speeds that are in a proportional relationship. For a proportional relationship, their speeds should maintain a constant ratio.

From the calculated speeds:

• Liam and Ashley have the same speed: 0.00163 miles/second.
• Taylor and Nathan both have the speed of approximately 0.00159 miles/second.

We can conclude that Liam, Ashley, Taylor, and Nathan are all in proportional relationships (specifically, Liam and Ashley have equal speeds, and Taylor and Nathan also have equal speeds).

Selected Student

Let's select Liam as one student from this group.