### 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 đť‘›. 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
Liamâ€™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 Jamesâ€™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.