Each Day, Jarrod Walks $1 \frac{3}{4}$ Miles To School And Back Home. Isaiah Walks $1 \frac{1}{3}$ Times As Far As Jarrod Walks. How Many Miles Does Isaiah Walk To School And Back Home Each Day?Write An Equation To Model The Problem.

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Introduction

In this article, we will explore a real-world problem involving distance and ratios. We will use mathematical equations to model the situation and find the solution. The problem involves two students, Jarrod and Isaiah, who walk different distances to school and back home each day.

The Problem

Jarrod walks 1341 \frac{3}{4} miles to school and back home each day. Isaiah walks 1131 \frac{1}{3} times as far as Jarrod walks. We need to find out how many miles Isaiah walks to school and back home each day.

Converting Mixed Numbers to Improper Fractions

To start solving the problem, we need to convert the mixed numbers to improper fractions. We can do this by multiplying the whole number part by the denominator and then adding the numerator.

  • Jarrod walks 1341 \frac{3}{4} miles, which is equal to (1Γ—4)+34=74\frac{(1 \times 4) + 3}{4} = \frac{7}{4} miles.
  • Isaiah walks 1131 \frac{1}{3} times as far as Jarrod walks, which is equal to 43Γ—74=73\frac{4}{3} \times \frac{7}{4} = \frac{7}{3} miles.

Writing an Equation to Model the Problem

Let's say the distance Isaiah walks to school and back home each day is xx miles. Since Isaiah walks 73\frac{7}{3} times as far as Jarrod walks, we can write an equation to model the problem:

x=73Γ—74x = \frac{7}{3} \times \frac{7}{4}

Simplifying the Equation

To simplify the equation, we can multiply the fractions:

x=7Γ—73Γ—4x = \frac{7 \times 7}{3 \times 4}

x=4912x = \frac{49}{12}

Finding the Distance Isaiah Walks

Now that we have the equation, we can find the distance Isaiah walks to school and back home each day. To do this, we can simplify the fraction:

x=4912x = \frac{49}{12}

x=4.0833x = 4.0833 miles (approximately)

Conclusion

In this article, we used mathematical equations to model a real-world problem involving distance and ratios. We converted mixed numbers to improper fractions, wrote an equation to model the problem, and simplified the equation to find the solution. We found that Isaiah walks approximately 4.0833 miles to school and back home each day.

Discussion

  • What if Jarrod walks a different distance to school and back home each day? How would this affect the equation?
  • What if Isaiah walks a different distance to school and back home each day? How would this affect the equation?
  • Can you think of other real-world problems that can be modeled using mathematical equations?

Additional Resources

  • Mathway: A online math problem solver that can help you solve equations and other math problems.
  • Khan Academy: A free online learning platform that offers math and other courses.
  • Math Open Reference: A free online math reference book that offers explanations and examples of various math concepts.
    Q&A: Understanding the Problem and Modeling with Equations ===========================================================

Introduction

In our previous article, we explored a real-world problem involving distance and ratios. We used mathematical equations to model the situation and find the solution. In this article, we will answer some frequently asked questions about the problem and provide additional insights.

Q: What if Jarrod walks a different distance to school and back home each day? How would this affect the equation?

A: If Jarrod walks a different distance to school and back home each day, the equation would change accordingly. Let's say Jarrod walks xx miles to school and back home each day. Then, Isaiah would walk 1131 \frac{1}{3} times as far as Jarrod walks, which is equal to 43Γ—x\frac{4}{3} \times x miles.

Q: What if Isaiah walks a different distance to school and back home each day? How would this affect the equation?

A: If Isaiah walks a different distance to school and back home each day, the equation would change accordingly. Let's say Isaiah walks yy miles to school and back home each day. Then, we can write an equation to model the problem:

y=43Γ—74y = \frac{4}{3} \times \frac{7}{4}

Q: Can you explain the concept of ratios in this problem?

A: Yes, the concept of ratios is crucial in this problem. A ratio is a comparison of two numbers or quantities. In this case, we are comparing the distance Isaiah walks to the distance Jarrod walks. The ratio of Isaiah's distance to Jarrod's distance is 43\frac{4}{3}, which means Isaiah walks 43\frac{4}{3} times as far as Jarrod walks.

Q: How do you convert mixed numbers to improper fractions?

A: To convert a mixed number to an improper fraction, we multiply the whole number part by the denominator and then add the numerator. For example, to convert 1341 \frac{3}{4} to an improper fraction, we multiply the whole number part (1) by the denominator (4) and then add the numerator (3):

134=(1Γ—4)+34=741 \frac{3}{4} = \frac{(1 \times 4) + 3}{4} = \frac{7}{4}

Q: What is the difference between a ratio and a proportion?

A: A ratio is a comparison of two numbers or quantities, while a proportion is a statement that two ratios are equal. In this problem, we are dealing with a ratio, which is the comparison of Isaiah's distance to Jarrod's distance. However, if we were to write an equation to model the problem, we would be dealing with a proportion, which is a statement that two ratios are equal.

Q: Can you provide more examples of real-world problems that can be modeled using mathematical equations?

A: Yes, here are a few examples:

  • A company produces two types of products, A and B. Product A requires 2 hours of labor and $100 of materials, while product B requires 3 hours of labor and $150 of materials. If the company produces 100 units of product A and 50 units of product B, how much will it cost to produce these products?
  • A car travels from city A to city B at an average speed of 60 miles per hour. If the distance between the two cities is 240 miles, how long will it take to travel from city A to city B?
  • A bakery sells two types of bread, whole wheat and white bread. The whole wheat bread costs $2.50 per loaf, while the white bread costs $3.00 per loaf. If the bakery sells 100 loaves of whole wheat bread and 50 loaves of white bread, how much will it earn in total?

Conclusion

In this article, we answered some frequently asked questions about the problem and provided additional insights. We also provided examples of real-world problems that can be modeled using mathematical equations. We hope this article has been helpful in understanding the concept of ratios and proportions in mathematical modeling.