# Question Video: Comparing Rates Using Tables Mathematics • 6th Grade

Use the table to determine which runners ran at the same rate.

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### Video Transcript

Use the table to determine which runners ran at the same rate.

In order to answer this question, we will look at the ratio of each runner of their time in hours to distance in miles. For Liam, this is two to 10. He jogged 10 miles in two hours. James’s ratio was three to 18 as he ran 18 miles in three hours. The corresponding ratios for David and Michael were four to 20 and three to 12, respectively. In order to compare two or more ratios, we need to write them in the form one to 𝑛. This is the unit rate or unit ratio. In this question, it will be the distance that each runner jogged in one hour.

For Liam, we will divide both sides of the ratio by two. This means that Liam ran a distance of five miles per hour. We divide the two parts of James’s ratio by three. This gives us a ratio of one to six. So, James ran six miles in one hour. Repeating this for David and Michael tells us that David ran five miles per hour and Michael ran four miles per hour. We’ve been asked to identify which runners ran at the same rate. As both Liam and David had the same unit ratio of one to five, we can conclude that they ran at the same rate.