How to Solve a One-Step Problem Involving Rates

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  • 0:01 What Is a Rate?
  • 1:06 How Can We Use Them?
  • 2:05 Process for Solving with Rates
  • 3:10 Examples
  • 4:37 Lesson Summary
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Lesson Transcript
Instructor: Kevin Newton

Kevin has edited encyclopedias, taught history, and has an MA in Islamic law/finance. He has since founded his own financial advice firm, Newton Analytical.

One of the most useful aspects of math is the ability to take a rate and use it to solve questions of time or quantity. In this lesson, we'll learn how to use rates, time, and quantity to solve for each other.

What Is a Rate?

Surely you've seen speed limit signs before. In black, bold writing they proclaim that you cannot legally go faster than the speed listed. Speed limits are really rate limits, as they limit the pace at which you can drive. A rate is just that, it is a definition of pace between two quantities. If the speed limit is 45 miles per hour, you can only go 45 miles in one hour. There is no limit on how many hours you can drive, but instead, it is an expression of what you can do in that hour.

Still, it's not just while driving that you are likely to encounter rates. If you go to the deli counter at a supermarket, you order meat and cheese in terms of pounds with the price listed. The price per pound is a rate. Something that is really important to notice about rates, however, is that they are almost always in terms of one of something. Speed limit signs are not posted in terms of fours of hours, but in terms of one hour. Likewise, deli meat is sold at a price per one pound, not a price per nine pounds.

How Can We Use Them?

This means that rates are remarkably useful things. We can quickly calculate how long it will take us to reach a destination by just knowing the distance to the goal. In short, they can effectively put an end to the chorus of 'Are we there yet?' from the back seat. Not only can rates calculate distances, but they can calculate costs. We can calculate costs of multiple pounds of ham by simply knowing the cost per pound. In short, rates allow us to quickly relate two different quantities to each other because they provide a link between the two.

Not only are rates useful, but they are remarkably easy to use. Remember how I said that rates almost always were in terms of one of something? That means that you don't have to think about too much cross-multiplying when using rates, since you'll be multiplying by one. If that doesn't make sense yet, don't worry about it - we're almost there! For now, just remember that as long as you can make sure that the units match up properly, you're good to go.

Process for Solving With Rates

Making sure that the units match up properly is where many people get tricked up when using rates. Remember, the units are there to help you. Sure, it may save you a little bit of paper space to not write down miles or miles per hour, but the units will really help you keep your thinking straight. So, how do you solve something using rates?

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