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Use the table to determine which runners ran at the same rate.
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In order to answer this question, we will look at the ratio of each runner of their time in hours to distance in miles.
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For Liam, this is two to 10.
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He jogged 10 miles in two hours.
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James’s ratio was three to 18 as he ran 18 miles in three hours.
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The corresponding ratios for David and Michael were four to 20 and three to 12, respectively.
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In order to compare two or more ratios, we need to write them in the form one to 𝑛.
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This is the unit rate or unit ratio.
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In this question, it will be the distance that each runner jogged in one hour.
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For Liam, we will divide both sides of the ratio by two.
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This means that Liam ran a distance of five miles per hour.
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We divide the two parts of James’s ratio by three.
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This gives us a ratio of one to six.
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So, James ran six miles in one hour.
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Repeating this for David and Michael tells us that David ran five miles per hour and Michael ran four miles per hour.
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We’ve been asked to identify which runners ran at the same rate.
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As both Liam and David had the same unit ratio of one to five, we can conclude that they ran at the same rate.