Form An Equation From The Word Problem And Solve To Answer The Question.Brian Drives 215 Miles At An Average Speed. He Then Travels 75 More Miles At A Speed Of 15 Miles Per Hour. If The Drive Times For Both Sections Of The Journey Are The Same,

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Introduction

Word problems are an essential part of mathematics, and they help us apply mathematical concepts to real-life situations. In this article, we will learn how to form an equation from a word problem and solve it to answer the question. We will use the example of Brian's road trip to demonstrate this process.

Understanding the Problem

Brian drives 215 miles at an average speed, and then he travels 75 more miles at a speed of 15 miles per hour. If the drive times for both sections of the journey are the same, we need to find the average speed for the first 215 miles.

Step 1: Identify the Variables

Let's identify the variables in the problem:

  • Distance 1: 215 miles
  • Distance 2: 75 miles
  • Speed 1: unknown (let's call it x miles per hour)
  • Speed 2: 15 miles per hour
  • Time 1: unknown (let's call it t hours)
  • Time 2: unknown (let's call it t hours)

Step 2: Form an Equation

Since the drive times for both sections of the journey are the same, we can set up an equation using the formula:

Time = Distance / Speed

We can write two equations:

  • Equation 1: t = 215 / x
  • Equation 2: t = 75 / 15

Step 3: Solve the Equation

We can simplify Equation 2 to find the value of t:

t = 75 / 15 t = 5 hours

Now that we have the value of t, we can substitute it into Equation 1:

5 = 215 / x

Step 4: Solve for x

To solve for x, we can multiply both sides of the equation by x:

5x = 215

Next, we can divide both sides of the equation by 5:

x = 215 / 5 x = 43 miles per hour

Conclusion

In this article, we learned how to form an equation from a word problem and solve it to answer the question. We used the example of Brian's road trip to demonstrate this process. By identifying the variables, forming an equation, and solving for the unknown, we were able to find the average speed for the first 215 miles.

Real-World Applications

Forming equations from word problems is a valuable skill that can be applied to many real-world situations. For example, in business, you may need to calculate the cost of production or the revenue generated by a product. In science, you may need to calculate the rate of a chemical reaction or the velocity of an object. By developing this skill, you can become a more effective problem-solver and make informed decisions in your personal and professional life.

Tips and Tricks

Here are some tips and tricks to help you form equations from word problems:

  • Read the problem carefully: Make sure you understand what the problem is asking for.
  • Identify the variables: Clearly define the variables in the problem.
  • Form an equation: Use the formula to set up an equation.
  • Solve the equation: Use algebraic techniques to solve for the unknown.
  • Check your answer: Make sure your answer makes sense in the context of the problem.

Common Mistakes

Here are some common mistakes to avoid when forming equations from word problems:

  • Not reading the problem carefully: Make sure you understand what the problem is asking for.
  • Not identifying the variables: Clearly define the variables in the problem.
  • Not forming an equation: Use the formula to set up an equation.
  • Not solving the equation: Use algebraic techniques to solve for the unknown.
  • Not checking your answer: Make sure your answer makes sense in the context of the problem.

Conclusion

Introduction

In our previous article, we learned how to form an equation from a word problem and solve it to answer the question. In this article, we will answer some frequently asked questions about forming equations from word problems.

Q: What is the first step in forming an equation from a word problem?

A: The first step in forming an equation from a word problem is to read the problem carefully and identify the variables. This involves clearly defining the variables in the problem, such as distance, speed, time, and cost.

Q: How do I know which variables to include in the equation?

A: To determine which variables to include in the equation, you need to understand what the problem is asking for. Ask yourself questions like "What is the unknown?" and "What information do I need to find the unknown?" This will help you identify the variables that are relevant to the problem.

Q: What is the difference between a variable and a constant?

A: A variable is a value that can change, while a constant is a value that remains the same. In a word problem, the variables are the values that you are trying to find, while the constants are the values that are given in the problem.

Q: How do I form an equation from a word problem?

A: To form an equation from a word problem, you need to use the formula that relates the variables. For example, if the problem involves distance, speed, and time, you can use the formula:

Time = Distance / Speed

This formula can be used to form an equation that relates the variables.

Q: What is the next step after forming an equation?

A: After forming an equation, the next step is to solve the equation for the unknown. This involves using algebraic techniques, such as addition, subtraction, multiplication, and division, to isolate the unknown variable.

Q: How do I know if my answer is correct?

A: To check if your answer is correct, you need to make sure that it makes sense in the context of the problem. Ask yourself questions like "Is the answer reasonable?" and "Does the answer match the information given in the problem?" If your answer does not make sense, you may need to re-evaluate your solution.

Q: What are some common mistakes to avoid when forming equations from word problems?

A: Some common mistakes to avoid when forming equations from word problems include:

  • Not reading the problem carefully
  • Not identifying the variables
  • Not forming an equation
  • Not solving the equation
  • Not checking the answer

Q: How can I practice forming equations from word problems?

A: To practice forming equations from word problems, you can try the following:

  • Read word problems and try to form equations from them
  • Use online resources, such as math websites and apps, to practice forming equations from word problems
  • Work with a tutor or teacher to practice forming equations from word problems
  • Use real-world examples, such as business or science problems, to practice forming equations from word problems

Conclusion

Forming equations from word problems is a valuable skill that can be applied to many real-world situations. By understanding the steps involved in forming an equation, you can become a more effective problem-solver and make informed decisions in your personal and professional life. Remember to read the problem carefully, identify the variables, form an equation, solve the equation, and check your answer. With practice and patience, you can become proficient in forming equations from word problems.

Additional Resources

  • Math websites: Websites such as Khan Academy, Mathway, and Wolfram Alpha offer interactive math lessons and practice problems.
  • Math apps: Apps such as Photomath, Math Tricks, and Math Games offer interactive math lessons and practice problems.
  • Tutors and teachers: Working with a tutor or teacher can provide personalized instruction and feedback.
  • Real-world examples: Using real-world examples, such as business or science problems, can provide practical experience in forming equations from word problems.