Rick Is Driving To His Uncle's House In Greensville, Which Is 120 Miles From Rick's Town. After Covering $x$ Miles, Rick Sees A Sign Stating That Greensville Is 20 Miles Away. Which Equation, When Solved, Will Give The Value Of
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Understanding the Problem
Rick is driving to his uncle's house in Greensville, which is 120 miles from Rick's town. After covering $x$ miles, Rick sees a sign stating that Greensville is 20 miles away. This means that the distance remaining to Greensville is 20 miles. We need to find the value of $x$, which represents the distance Rick has already covered.
Setting Up the Equation
To solve for $x$, we need to set up an equation that represents the situation. We know that the total distance to Greensville is 120 miles, and the distance remaining is 20 miles. This means that the distance Rick has already covered, $x$, plus the distance remaining, 20 miles, is equal to the total distance, 120 miles.
The Equation
The equation can be written as:
Solving for x
To solve for $x$, we need to isolate the variable $x$ on one side of the equation. We can do this by subtracting 20 from both sides of the equation.
This simplifies to:
Checking the Solution
To check our solution, we can plug in the value of $x$ into the original equation and see if it is true.
This is indeed true, so we can be confident that our solution is correct.
Conclusion
In this problem, we used algebra to solve for the distance Rick has already covered. We set up an equation based on the situation, solved for the variable $x$, and checked our solution to make sure it was correct. This is a great example of how algebra can be used to solve real-world problems.
Real-World Applications
This problem has many real-world applications. For example, if you are driving to a destination and you see a sign that says the distance remaining is 20 miles, you can use this equation to figure out how far you have already traveled. This can be useful for planning your trip, estimating your arrival time, and making sure you have enough gas to make it to your destination.
Tips and Tricks
- When setting up an equation, make sure to read the problem carefully and identify the variables and constants.
- Use algebraic properties, such as the commutative and associative properties, to simplify the equation.
- Check your solution by plugging it back into the original equation.
- Use real-world examples to help you understand and apply the concept.
Common Mistakes
- Failing to read the problem carefully and identify the variables and constants.
- Not using algebraic properties to simplify the equation.
- Not checking the solution by plugging it back into the original equation.
- Not using real-world examples to help you understand and apply the concept.
Practice Problems
- A car is traveling at a speed of 60 miles per hour. If it has already traveled 120 miles, how much farther does it need to travel to reach its destination?
- A plane is flying at a speed of 500 miles per hour. If it has already traveled 200 miles, how much farther does it need to travel to reach its destination?
- A train is traveling at a speed of 80 miles per hour. If it has already traveled 160 miles, how much farther does it need to travel to reach its destination?
Conclusion
In this article, we used algebra to solve for the distance Rick has already covered. We set up an equation based on the situation, solved for the variable $x$, and checked our solution to make sure it was correct. This is a great example of how algebra can be used to solve real-world problems. We also discussed real-world applications, tips and tricks, and common mistakes to help you understand and apply the concept. Finally, we provided practice problems to help you practice and reinforce your understanding of the concept.
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Frequently Asked Questions
Q: What is the equation that represents the situation?
A: The equation that represents the situation is $x + 20 = 120$, where $x$ is the distance Rick has already covered.
Q: How do I solve for x?
A: To solve for $x$, you need to isolate the variable $x$ on one side of the equation. You can do this by subtracting 20 from both sides of the equation.
Q: What is the value of x?
A: The value of $x$ is 100.
Q: How do I check my solution?
A: To check your solution, you can plug in the value of $x$ into the original equation and see if it is true.
Q: What are some real-world applications of this problem?
A: This problem has many real-world applications, such as planning a trip, estimating arrival time, and making sure you have enough gas to make it to your destination.
Q: What are some tips and tricks for solving this problem?
A: Some tips and tricks for solving this problem include:
- Reading the problem carefully and identifying the variables and constants.
- Using algebraic properties, such as the commutative and associative properties, to simplify the equation.
- Checking your solution by plugging it back into the original equation.
- Using real-world examples to help you understand and apply the concept.
Q: What are some common mistakes to avoid?
A: Some common mistakes to avoid include:
- Failing to read the problem carefully and identify the variables and constants.
- Not using algebraic properties to simplify the equation.
- Not checking the solution by plugging it back into the original equation.
- Not using real-world examples to help you understand and apply the concept.
Q: Can you provide some practice problems?
A: Yes, here are some practice problems:
- A car is traveling at a speed of 60 miles per hour. If it has already traveled 120 miles, how much farther does it need to travel to reach its destination?
- A plane is flying at a speed of 500 miles per hour. If it has already traveled 200 miles, how much farther does it need to travel to reach its destination?
- A train is traveling at a speed of 80 miles per hour. If it has already traveled 160 miles, how much farther does it need to travel to reach its destination?
Conclusion
In this article, we provided a Q&A section to help you understand and apply the concept of solving for distance. We answered frequently asked questions, provided tips and tricks, and discussed common mistakes to avoid. We also provided practice problems to help you practice and reinforce your understanding of the concept.
Additional Resources
- For more practice problems, check out our practice problems page.
- For more information on algebra, check out our algebra page.
- For more information on real-world applications, check out our real-world applications page.
Conclusion
We hope this Q&A article has been helpful in understanding and applying the concept of solving for distance. If you have any further questions or need additional help, please don't hesitate to contact us.