Video: Comparing Unit Rates

Michael wants to sign up for his school’s sports competition. In order to be accepted, he has to be able to run 400 meters in 1 minute. Michael took 20 seconds to run 100 meters. If he could run at the same rate, would he qualify to take part?

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Video Transcript

Michael wants to sign up for his school’s sports competition. In order to be accepted, he has to be able to run 400 meters in one minute. Michael took 20 seconds to run 100 meters. If he could run at the same rate, would he qualify to take part?

We’re told in the question that Michael needs to be able to run 400 meters in one minute. If we write this as a ratio of time in minutes to distance in meters, this would be one to 400. We’re also told that Michael can run 100 meters in 20 seconds. There are 60 seconds in one minute. And 20 multiplied by three is equal to 60. Multiplying 100 by three gives us 300. So, if Michael runs at the same rate, he will cover 300 meters in 60 seconds. This ratio of time in minutes to distance in meters is one to 300.

As Michael needed to cover a distance of 400 meters in one minute, the correct answer is no. He would not qualify to take part. Writing any ratio in this form, one to 𝑛, is known as the unit ratio or unit rate. For every one unit, or minute in this case, of time, we can see the distance in meters that Michael covered.

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