# Video: Using Unit Rate to Compare Three Rates

Mason, Liam, and James are biking. Mason can bike 2 miles in 20 minutes, Liam can bike 3 miles in 25 minutes, and James can bike 6 miles in 66 minutes. Who cycles at the fastest rate?

02:26

### Video Transcript

Mason, Liam, and James are biking. Mason can bike two miles in 20 minutes, Liam can bike three miles in 25 minutes, and James can bike six miles in 66 minutes. Who cycles at the fastest rate?

In order to compare the three speeds, we will write the ratio of distance in miles to time in minutes. For Mason, this is a ratio of two to 20. For Liam, the ratio is three to 25. And finally, for James, the ratio is six to 66. In order to compare the three ratios, we need to calculate the unit rate or unit ratio. This is written in the form one to 𝑛. In this question, this will calculate the time it would take each boy to cycle a distance of one mile. When simplifying or finding equivalent ratios, we need to multiply or divide both sides by the same number. For mason, we need to divide both sides by two. This means that the ratio two to 20 is equivalent to one to 10. It takes Mason 10 minutes to bike one mile.

To make the left-hand side of Liam’s ratio equal to one, we need to divide both sides by three. 25 divided by three is equal to eight and one-third or 8.3 recurring, written with a dot or bar above the three. It takes Liam eight and a third minutes to cycle one mile. Dividing both sides of James’s ratio by six gives us the new ratio one to 11. It takes James 11 minutes to cycle one mile. As all three ratios are now written in terms of their unit rate, we can compare them. The person who cycles at the fastest rate will be the person who takes the least amount of time to cycle one mile. In this question, this is Liam.