In Questions 4 And 5, Use Unit Rates To Solve.4. A Football Player Runs 80 Yards In 25 Seconds. If He Maintains The Same Rate Of Speed, How Far Could He Run In 60 Seconds?

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Understanding Unit Rates

Unit rates are a fundamental concept in mathematics that help us compare different quantities. In this article, we will explore how to use unit rates to solve problems, specifically in the context of a football player's running speed.

What is a Unit Rate?

A unit rate is a ratio of two quantities, where the second quantity is expressed as a unit of the first quantity. For example, if a football player runs 80 yards in 25 seconds, the unit rate would be 80 yards per 25 seconds. This means that for every 25 seconds, the player runs 80 yards.

Using Unit Rates to Solve Problems

Now that we understand what a unit rate is, let's apply this concept to solve the problem presented in question 4.

Problem 4

A football player runs 80 yards in 25 seconds. If he maintains the same rate of speed, how far could he run in 60 seconds?

Step 1: Identify the Unit Rate

To solve this problem, we need to identify the unit rate of the football player's running speed. We are given that he runs 80 yards in 25 seconds, so the unit rate is 80 yards per 25 seconds.

Step 2: Convert the Unit Rate to a More Convenient Form

To make it easier to work with, we can convert the unit rate to a more convenient form. We can divide both the numerator and the denominator by 5, which gives us a unit rate of 16 yards per 5 seconds.

Step 3: Use the Unit Rate to Solve the Problem

Now that we have the unit rate, we can use it to solve the problem. We are asked to find out how far the football player could run in 60 seconds. To do this, we can multiply the unit rate by the number of 5-second intervals in 60 seconds.

There are 12 intervals of 5 seconds in 60 seconds (60 ÷ 5 = 12). We can multiply the unit rate by 12 to get the total distance:

16 yards/5 seconds × 12 = 192 yards

Therefore, the football player could run 192 yards in 60 seconds.

Conclusion

In this article, we learned how to use unit rates to solve problems. We applied this concept to a real-world scenario, where a football player's running speed was given in terms of a unit rate. By identifying the unit rate, converting it to a more convenient form, and using it to solve the problem, we were able to find the answer.

Real-World Applications of Unit Rates

Unit rates have many real-world applications, including:

  • Finance: Unit rates are used to calculate interest rates, investment returns, and other financial metrics.
  • Science: Unit rates are used to measure the rate of change of physical quantities, such as velocity and acceleration.
  • Engineering: Unit rates are used to design and optimize systems, such as electrical circuits and mechanical systems.

Common Mistakes to Avoid

When working with unit rates, there are several common mistakes to avoid:

  • Not converting the unit rate to a more convenient form: This can make it difficult to work with the unit rate and may lead to errors.
  • Not using the correct unit rate: Make sure to use the correct unit rate for the problem at hand.
  • Not checking units: Always check the units of the quantities involved to ensure that they are consistent.

Practice Problems

Here are some practice problems to help you apply what you have learned:

  • A car travels 120 miles in 4 hours. If it maintains the same rate of speed, how far could it travel in 6 hours?
  • A bicycle travels 20 miles in 2 hours. If it maintains the same rate of speed, how far could it travel in 4 hours?

Conclusion

Frequently Asked Questions

In this article, we will answer some of the most frequently asked questions about unit rates.

Q: What is a unit rate?

A: A unit rate is a ratio of two quantities, where the second quantity is expressed as a unit of the first quantity. For example, if a football player runs 80 yards in 25 seconds, the unit rate would be 80 yards per 25 seconds.

Q: How do I calculate a unit rate?

A: To calculate a unit rate, you need to divide the first quantity by the second quantity. For example, if a car travels 120 miles in 4 hours, the unit rate would be 120 miles ÷ 4 hours = 30 miles per hour.

Q: What is the difference between a unit rate and a ratio?

A: A unit rate is a ratio where the second quantity is expressed as a unit of the first quantity. For example, if a football player runs 80 yards in 25 seconds, the unit rate would be 80 yards per 25 seconds. A ratio, on the other hand, is a comparison of two quantities without expressing the second quantity as a unit of the first quantity. For example, if a football player runs 80 yards in 25 seconds, the ratio would be 80 yards to 25 seconds.

Q: How do I use unit rates to solve problems?

A: To use unit rates to solve problems, you need to identify the unit rate, convert it to a more convenient form if necessary, and then use it to solve the problem. For example, if a football player runs 80 yards in 25 seconds, and you want to know how far he could run in 60 seconds, you can use the unit rate to solve the problem.

Q: What are some common mistakes to avoid when working with unit rates?

A: Some common mistakes to avoid when working with unit rates include:

  • Not converting the unit rate to a more convenient form
  • Not using the correct unit rate
  • Not checking units
  • Not using the unit rate to solve the problem

Q: How do I convert a unit rate to a more convenient form?

A: To convert a unit rate to a more convenient form, you can divide both the numerator and the denominator by a common factor. For example, if a car travels 120 miles in 4 hours, the unit rate would be 120 miles ÷ 4 hours = 30 miles per hour. You can then convert this unit rate to a more convenient form by dividing both the numerator and the denominator by 10, which gives you 3 miles per hour.

Q: What are some real-world applications of unit rates?

A: Unit rates have many real-world applications, including:

  • Finance: Unit rates are used to calculate interest rates, investment returns, and other financial metrics.
  • Science: Unit rates are used to measure the rate of change of physical quantities, such as velocity and acceleration.
  • Engineering: Unit rates are used to design and optimize systems, such as electrical circuits and mechanical systems.

Q: How do I practice using unit rates to solve problems?

A: To practice using unit rates to solve problems, you can try the following:

  • Use online resources, such as math websites and apps, to practice solving problems involving unit rates.
  • Work with a tutor or teacher to practice solving problems involving unit rates.
  • Try solving problems involving unit rates on your own, using a calculator or other tools as needed.

Conclusion

In this article, we answered some of the most frequently asked questions about unit rates. We discussed what a unit rate is, how to calculate a unit rate, and how to use unit rates to solve problems. We also discussed common mistakes to avoid when working with unit rates and provided some real-world applications of unit rates. With practice, you will become proficient in using unit rates to solve problems and apply this concept to a wide range of situations.