Florian Ran 1.2 Miles And Walked 4.8 Laps Around The Path At The Park For A Total Distance Of 3.6 Miles. Which Shows The Correct Equation And Value Of { X $} , T H E D I S T A N C E O F 1 L A P A R O U N D T H E P A T H A T T H E P A R K ? A . \[ , The Distance Of 1 Lap Around The Path At The Park?A. \[ , T H E D I S T An Ceo F 1 L A P A Ro U N D T H E P A T Ha Tt H E P A R K ? A . \[ 3.6x + 1.2 = 4.8; ,
Introduction
In this problem, we are given that Florian ran 1.2 miles and walked 4.8 laps around the path at the park for a total distance of 3.6 miles. We need to find the distance of one lap around the path at the park, denoted by { x $}$. To solve this problem, we will use algebraic equations to represent the given information and then solve for the unknown variable.
Given Information
- Florian ran 1.2 miles
- Florian walked 4.8 laps around the path at the park
- The total distance covered is 3.6 miles
Equation Representation
Let's represent the given information using algebraic equations. We know that the total distance covered is the sum of the distance covered by running and walking. Since Florian walked 4.8 laps, we can represent the distance covered by walking as 4.8 times the distance of one lap, which is { 4.8x $}$. Therefore, the equation representing the total distance covered is:
{ 1.2 + 4.8x = 3.6 $}$
Solving the Equation
To solve for { x $}$, we need to isolate the variable on one side of the equation. We can do this by subtracting 1.2 from both sides of the equation:
{ 4.8x = 3.6 - 1.2 $}$
{ 4.8x = 2.4 $}$
Next, we can divide both sides of the equation by 4.8 to solve for { x $}$:
{ x = \frac{2.4}{4.8} $}$
{ x = 0.5 $}$
Conclusion
Therefore, the distance of one lap around the path at the park is 0.5 miles.
Discussion
This problem involves using algebraic equations to represent real-world situations and solving for unknown variables. It requires a basic understanding of algebraic operations, such as addition, subtraction, multiplication, and division. The problem also involves interpreting the given information and representing it using mathematical equations.
Key Takeaways
- Algebraic equations can be used to represent real-world situations.
- Solving for unknown variables involves isolating the variable on one side of the equation.
- Basic algebraic operations, such as addition, subtraction, multiplication, and division, are essential for solving equations.
Additional Examples
- A car travels 250 miles in 5 hours. What is the average speed of the car?
- A bakery sells 500 loaves of bread per day. If each loaf costs $2, how much money does the bakery make in a day?
- A person invests $1000 in a savings account that earns an interest rate of 5% per year. How much money will the person have in the account after 2 years?
Q: What is the distance of one lap around the path at the park?
A: The distance of one lap around the path at the park is 0.5 miles.
Q: How did you solve for the distance of one lap?
A: We used an algebraic equation to represent the given information. The equation was { 1.2 + 4.8x = 3.6 $}$. We then solved for { x $}$ by subtracting 1.2 from both sides of the equation, dividing both sides by 4.8, and isolating the variable on one side of the equation.
Q: What is the total distance covered by Florian?
A: The total distance covered by Florian is 3.6 miles.
Q: How many laps did Florian walk around the path at the park?
A: Florian walked 4.8 laps around the path at the park.
Q: How many miles did Florian run?
A: Florian ran 1.2 miles.
Q: What is the relationship between the distance of one lap and the total distance covered?
A: The distance of one lap is a factor of the total distance covered. In this case, the distance of one lap is multiplied by the number of laps walked to get the total distance covered.
Q: Can you provide more examples of how to use algebraic equations to solve real-world problems?
A: Yes, here are a few examples:
- A person invests $1000 in a savings account that earns an interest rate of 5% per year. How much money will the person have in the account after 2 years?
- A bakery sells 500 loaves of bread per day. If each loaf costs $2, how much money does the bakery make in a day?
- A car travels 250 miles in 5 hours. What is the average speed of the car?
Q: What are some common algebraic operations used to solve equations?
A: Some common algebraic operations used to solve equations include:
- Addition
- Subtraction
- Multiplication
- Division
- Exponents
- Roots
Q: How do you know which algebraic operation to use when solving an equation?
A: The choice of algebraic operation depends on the specific equation and the information given. In general, you need to isolate the variable on one side of the equation by performing the necessary algebraic operations.
Q: Can you provide more tips and tricks for solving algebraic equations?
A: Yes, here are a few tips and tricks:
- Read the equation carefully and identify the variable you need to solve for.
- Use inverse operations to isolate the variable on one side of the equation.
- Simplify the equation by combining like terms.
- Check your solution by plugging it back into the original equation.
Q: What are some common mistakes to avoid when solving algebraic equations?
A: Some common mistakes to avoid when solving algebraic equations include:
- Not reading the equation carefully and identifying the variable you need to solve for.
- Not using inverse operations to isolate the variable on one side of the equation.
- Not simplifying the equation by combining like terms.
- Not checking your solution by plugging it back into the original equation.
By following these tips and tricks, you can improve your skills in solving algebraic equations and become more confident in your ability to solve real-world problems.