Alonso walked with his friend Andy one day, and wanted to compare their speeds. Alonso walked 3 miles in one hour, and Andy walked 2 miles in 2 hours. Complete the table to graph the relationship for each person.

What is the constant of proportionality for Alonso?
3
What is the constant of proportionality for Andy?
Who walked faster?

1 answer

To find the constant of proportionality for both Alonso and Andy, we can calculate their speeds in miles per hour.

Alonso:

  • Distance: 3 miles
  • Time: 1 hour

To find the speed (constant of proportionality), we use the formula: \[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{3 \text{ miles}}{1 \text{ hour}} = 3 \text{ miles per hour} \] So, the constant of proportionality for Alonso is 3.

Andy:

  • Distance: 2 miles
  • Time: 2 hours

To find Andy's speed: \[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{2 \text{ miles}}{2 \text{ hours}} = 1 \text{ mile per hour} \] So, the constant of proportionality for Andy is 1.

Comparison of Speeds:

  • Alonso's speed: 3 miles per hour
  • Andy's speed: 1 mile per hour

Who walked faster? Alonso walked faster, as he walked at a speed of 3 miles per hour, compared to Andy's 1 mile per hour.

Summary:

  • Constant of proportionality for Alonso: 3
  • Constant of proportionality for Andy: 1
  • Who walked faster: Alonso