Emilie Rides Her Bike $x$ Miles Before She Gets A Flat Tire. She Walks $\frac{1}{3}$ Mile To A Bus Stop And Then Takes A Bus For $2 \frac{1}{2}$ Miles.Which Expression Shows How Many Miles Emilie Travels In Total?A. $x +

Introduction

In this article, we will delve into the world of mathematics and explore a scenario where Emilie rides her bike, gets a flat tire, and then continues her journey on foot and by bus. We will analyze the situation and determine the expression that represents the total distance traveled by Emilie.

The Scenario

Emilie rides her bike $x$ miles before she gets a flat tire. This is the initial distance she covers on her bike. After the flat tire, she walks $\frac{1}{3}$ mile to a bus stop. This is the distance she covers on foot. Finally, she takes a bus for $2 \frac{1}{2}$ miles. This is the distance she covers by bus.

Calculating the Total Distance

To find the total distance traveled by Emilie, we need to add up the distances covered on her bike, on foot, and by bus. Let's break it down step by step:

• The distance covered on her bike is $x$ miles.
• The distance covered on foot is $\frac{1}{3}$ mile.
• The distance covered by bus is $2 \frac{1}{2}$ miles, which can be written as $\frac{5}{2}$ miles.

Now, let's add up these distances to find the total distance traveled by Emilie:

$$\text{Total distance} = x + \frac{1}{3} + \frac{5}{2}$$

To add these fractions, we need to find a common denominator. The least common multiple of 3 and 2 is 6. So, we can rewrite the fractions with a common denominator of 6:

$$\frac{1}{3} = \frac{2}{6}$$

$$\frac{5}{2} = \frac{15}{6}$$

Now, we can add the fractions:

$$\text{Total distance} = x + \frac{2}{6} + \frac{15}{6}$$

$$\text{Total distance} = x + \frac{17}{6}$$

Conclusion

In conclusion, the expression that shows how many miles Emilie travels in total is $x + \frac{17}{6}$. This expression represents the sum of the distances covered on her bike, on foot, and by bus.

Discussion

This problem is a great example of how mathematics can be applied to real-life scenarios. By breaking down the situation into smaller parts and using mathematical concepts, we can determine the total distance traveled by Emilie.

Key Takeaways

• The distance covered on her bike is $x$ miles.
• The distance covered on foot is $\frac{1}{3}$ mile.
• The distance covered by bus is $2 \frac{1}{2}$ miles, which can be written as $\frac{5}{2}$ miles.
• The total distance traveled by Emilie is represented by the expression $x + \frac{17}{6}$.

Further Exploration

This problem can be extended to explore other mathematical concepts, such as:

• Converting mixed numbers to improper fractions
• Adding and subtracting fractions with different denominators
• Using variables to represent unknown values

Introduction

In our previous article, we explored the scenario of Emilie riding her bike, getting a flat tire, and then continuing her journey on foot and by bus. We determined the expression that represents the total distance traveled by Emilie. In this article, we will answer some frequently asked questions related to this scenario.

Q&A

Q: What is the initial distance covered by Emilie on her bike?

A: The initial distance covered by Emilie on her bike is $x$ miles.

Q: How far does Emilie walk to a bus stop after getting a flat tire?

A: Emilie walks $\frac{1}{3}$ mile to a bus stop after getting a flat tire.

Q: How far does Emilie travel by bus?

A: Emilie travels $2 \frac{1}{2}$ miles by bus, which can be written as $\frac{5}{2}$ miles.

Q: What is the total distance traveled by Emilie?

A: The total distance traveled by Emilie is represented by the expression $x + \frac{17}{6}$.

Q: Can you explain the concept of adding fractions with different denominators?

A: Yes, when adding fractions with different denominators, we need to find a common denominator. The least common multiple of the denominators is the common denominator. We can then rewrite the fractions with the common denominator and add them.

Q: How do you convert a mixed number to an improper fraction?

A: To convert a mixed number to an improper fraction, we multiply the whole number by the denominator and add the numerator. We then write the result as an improper fraction.

Q: Can you provide an example of converting a mixed number to an improper fraction?

A: Yes, let's consider the mixed number $2 \frac{1}{2}$. To convert it to an improper fraction, we multiply the whole number by the denominator and add the numerator:

$$2 \times 2 + 1 = 5$$

So, the improper fraction is $\frac{5}{2}$.

Q: How do you add and subtract fractions with different denominators?

A: To add or subtract fractions with different denominators, we need to find a common denominator. We can then rewrite the fractions with the common denominator and add or subtract them.

Q: Can you provide an example of adding fractions with different denominators?

A: Yes, let's consider the fractions $\frac{1}{3}$ and $\frac{5}{2}$. To add them, we need to find a common denominator, which is 6. We can then rewrite the fractions with the common denominator and add them:

$$\frac{1}{3} = \frac{2}{6}$$

$$\frac{5}{2} = \frac{15}{6}$$

$$\frac{2}{6} + \frac{15}{6} = \frac{17}{6}$$

Conclusion

In conclusion, we have answered some frequently asked questions related to the scenario of Emilie riding her bike, getting a flat tire, and then continuing her journey on foot and by bus. We have also explored the concepts of adding fractions with different denominators, converting mixed numbers to improper fractions, and adding and subtracting fractions with different denominators.

Key Takeaways

• The initial distance covered by Emilie on her bike is $x$ miles.
• The distance covered on foot is $\frac{1}{3}$ mile.
• The distance covered by bus is $2 \frac{1}{2}$ miles, which can be written as $\frac{5}{2}$ miles.
• The total distance traveled by Emilie is represented by the expression $x + \frac{17}{6}$.
• To add fractions with different denominators, we need to find a common denominator.
• To convert a mixed number to an improper fraction, we multiply the whole number by the denominator and add the numerator.
• To add and subtract fractions with different denominators, we need to find a common denominator.