There Are Two Routes Lucas Can Take To Walk To School. Route { A $}$ Is { 2 \frac{1}{8} $}$ Miles And Is { \frac{3}{8} $}$ Mile Longer Than Route { B $} . T H E E Q U A T I O N \[ . The Equation \[ . T H Ee Q U A T I O N \[ B + \frac{3}{8} = 2 \frac{1}{8}
Introduction
As a student, Lucas has to walk to school every day. He has two routes to choose from, and each route has its own distance. In this article, we will explore the two routes and determine which one is longer. We will use mathematical equations to solve the problem and find the distance of each route.
Route A and Route B
Route A is 2 1/8 miles long, and Route B is x miles long. We are given that Route A is 3/8 mile longer than Route B. We can write an equation to represent this relationship:
b + 3/8 = 2 1/8
Solving the Equation
To solve the equation, we need to isolate the variable x. We can start by converting the mixed numbers to improper fractions:
2 1/8 = 17/8
Now, we can rewrite the equation:
b + 3/8 = 17/8
Next, we can subtract 3/8 from both sides of the equation:
b = 17/8 - 3/8
To subtract fractions, we need to have the same denominator. In this case, the denominator is 8. We can rewrite the fractions with the same denominator:
b = 17/8 - 6/8
Now, we can subtract the numerators:
b = 11/8
Conclusion
We have solved the equation and found the distance of Route B. Route B is 11/8 miles long. We can also find the distance of Route A by adding 3/8 to the distance of Route B:
Route A = Route B + 3/8 = 11/8 + 3/8 = 14/8 = 1 3/4
Comparison of the Two Routes
Now that we have the distances of both routes, we can compare them. Route A is 1 3/4 miles long, and Route B is 11/8 miles long. We can convert both distances to decimal form to make the comparison easier:
Route A = 1.75 miles Route B = 1.375 miles
As we can see, Route A is longer than Route B by 0.375 miles.
Real-World Applications
This problem may seem simple, but it has real-world applications. For example, if you are planning a road trip, you need to know the distance between two points. You can use the same method to find the distance between two points on a map.
Tips and Tricks
When solving equations, it's essential to follow the order of operations (PEMDAS):
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate any multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
By following the order of operations, you can ensure that you are solving the equation correctly.
Conclusion
In conclusion, we have solved the equation and found the distance of Route B. We have also compared the two routes and found that Route A is longer than Route B. This problem has real-world applications, and by following the order of operations, you can ensure that you are solving equations correctly.
Additional Resources
If you want to learn more about solving equations, I recommend checking out the following resources:
- Khan Academy: Solving Equations
- Mathway: Solving Equations
- IXL: Solving Equations
These resources provide step-by-step instructions and examples to help you learn how to solve equations.
Final Thoughts
Q: What is the difference between Route A and Route B?
A: Route A is 2 1/8 miles long, and Route B is x miles long. Route A is 3/8 mile longer than Route B.
Q: How do I solve the equation b + 3/8 = 2 1/8?
A: To solve the equation, you need to isolate the variable x. You can start by converting the mixed numbers to improper fractions:
2 1/8 = 17/8
Then, you can rewrite the equation:
b + 3/8 = 17/8
Next, you can subtract 3/8 from both sides of the equation:
b = 17/8 - 3/8
To subtract fractions, you need to have the same denominator. In this case, the denominator is 8. You can rewrite the fractions with the same denominator:
b = 17/8 - 6/8
Now, you can subtract the numerators:
b = 11/8
Q: What is the distance of Route B?
A: The distance of Route B is 11/8 miles.
Q: How do I convert the distance of Route B to decimal form?
A: To convert the distance of Route B to decimal form, you can divide the numerator by the denominator:
11/8 = 1.375
Q: What is the difference in distance between Route A and Route B?
A: Route A is 1 3/4 miles long, and Route B is 1.375 miles long. The difference in distance between Route A and Route B is 0.375 miles.
Q: What are some real-world applications of solving equations?
A: Solving equations has many real-world applications, such as:
- Finding the distance between two points on a map
- Calculating the cost of a product or service
- Determining the amount of time it takes to complete a task
- Solving problems in physics, engineering, and other fields
Q: What are some tips and tricks for solving equations?
A: Here are some tips and tricks for solving equations:
- Follow the order of operations (PEMDAS)
- Use the correct techniques for solving equations, such as adding, subtracting, multiplying, and dividing
- Check your work by plugging in the solution to the original equation
- Practice regularly to build your skills and confidence
Q: Where can I find additional resources for learning about solving equations?
A: Here are some additional resources for learning about solving equations:
- Khan Academy: Solving Equations
- Mathway: Solving Equations
- IXL: Solving Equations
- Online tutorials and videos
- Math textbooks and workbooks
Q: What are some common mistakes to avoid when solving equations?
A: Here are some common mistakes to avoid when solving equations:
- Not following the order of operations (PEMDAS)
- Not using the correct techniques for solving equations
- Not checking your work by plugging in the solution to the original equation
- Not practicing regularly to build your skills and confidence
Q: How can I improve my skills in solving equations?
A: Here are some ways to improve your skills in solving equations:
- Practice regularly
- Review and practice different types of equations
- Seek help from a teacher, tutor, or online resource
- Join a study group or math club
- Take online courses or tutorials to learn new skills and techniques.