Question

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?

Answer 1

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:

`\frac{400\hspace{4}meters}{1.5\hspace{4}minutes}` and
`\frac{800\hspace{4}meters}{3\hspace{4}minutes}`

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

Multiply the first ratio by
`\frac{2}2`:

`\frac{400\hspace{4}meters}{1.5\hspace{4}minutes}*(2)/(2)\\\\= \frac{800\hspace{4}meters}{3\hspace{4}minutes}`

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.