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Joe ran 400 meters in 1.5 minutes and 800 meters in 3 minutes. Is there a proportional relationship between number of meters Joe ran the number of minutes he ran?

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Proportional Relationships

The relationship between two variables are proportional if their ratios are equivalent (taken from Khan Academy).

To determine whether or not a relationship is proportional, we can see if two given ratios are the same.

Solving the Question

We're given:

  • Joe ran 400 meters in 1.5 minutes
  • Joe ran 800 meters in 3 minutes

These pieces of information are ratios. We can write them in the following format:

[tex]\dfrac{400\hspace{4}meters}{1.5\hspace{4}minutes}[/tex] and [tex]\dfrac{800\hspace{4}meters}{3\hspace{4}minutes}[/tex]

We can see if they're equivalent by finding a common denominator.

Multiply the first ratio by [tex]\dfrac{2}2[/tex]:

[tex]\dfrac{400\hspace{4}meters}{1.5\hspace{4}minutes}*\dfrac{2}{2}\\\\= \dfrac{800\hspace{4}meters}{3\hspace{4}minutes}[/tex]

The ratios are equivalent. Therefore, the relationship between the number of meters Joe ran and the number of minutes he ran is proportional.

Answer

Yes, there is a proportional relationship.

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