Rate is a measure of the speed or pace at which something occurs or changes over time. It quantifies the change in a variable relative to the change in another variable, often time.
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The concept of rate is central to solving percent applications, uniform motion problems, and work-related problems.
In percent applications, the rate is often expressed as a percentage, which represents a comparison to a whole or base value.
In uniform motion problems, the rate is the speed or velocity, which represents the distance traveled per unit of time.
In work-related problems, the rate can represent the amount of work done per unit of time, or the cost per unit of a product or service.
Understanding the underlying rate in a problem is crucial for setting up the appropriate equation or proportion to solve for the unknown quantity.
Review Questions
Explain how the concept of rate is used in solving percent applications.
In percent applications, the rate is often expressed as a percentage, which represents a comparison to a whole or base value. For example, in a problem asking what 25% of $80 is, the rate of 25% is used to set up a proportion or equation to find the unknown quantity. The rate of 25% indicates that the desired value is 25 parts out of 100 parts of the whole, which can then be used to calculate the actual dollar amount.
Describe the role of rate in solving uniform motion problems.
In uniform motion problems, the rate is the speed or velocity, which represents the distance traveled per unit of time. This rate is a key variable in the formula for uniform motion, which states that distance = rate × time. By knowing any two of these variables, you can solve for the third. For example, if you know the distance traveled and the time, you can calculate the rate of speed or velocity.
Analyze how rate is used in solving work-related problems.
In work-related problems, the rate can represent the amount of work done per unit of time, or the cost per unit of a product or service. For instance, if a worker can produce 50 widgets in 2 hours, the rate of production would be 25 widgets per hour. Similarly, if a product costs $15 for 3 pounds, the rate would be $5 per pound. Understanding these rates is crucial for setting up the appropriate equations or proportions to solve for unknown quantities, such as the total work done, the time required, or the cost of a certain quantity of the product.