Understanding the Time Spent on Weight Machines

Oct 13, 2025 by miodeya.com 88 views

Introduction

In this article, we will delve into the world of mathematics and explore a real-life scenario involving time and fractions. Our protagonist, Leo, spent a significant amount of time working out at the gym, and we will use mathematical equations to determine the correct representation of his workout time.

The Problem

Leo spent the same amount of time working on each of 5 different weight machines and then spent $\frac{2}{3}$ of an hour on the treadmill. If he spent a total of $1 \frac{3}{4}$ hours at the gym, we need to find the correct equation that represents the total time spent at the gym.

Understanding the Time Spent on Weight Machines

Let's denote the time spent on each weight machine as $x$ . Since Leo spent the same amount of time on each machine, the total time spent on all 5 machines is $5x$ .

Understanding the Time Spent on the Treadmill

Leo spent $\frac{2}{3}$ of an hour on the treadmill. To convert this to a decimal, we can divide the numerator by the denominator: $\frac{2}{3} = 0.6667$ hours.

Understanding the Total Time Spent at the Gym

The total time spent at the gym is given as $1 \frac{3}{4}$ hours. To convert this to an improper fraction, we can multiply the whole number by the denominator and add the numerator: $1 \frac{3}{4} = \frac{7}{4}$ hours.

Setting Up the Equation

We can now set up an equation to represent the total time spent at the gym. The equation is:

5x + \frac{2}{3} = \frac{7}{4}

Solving the Equation

To solve for $x$ , we need to isolate the variable. We can start by subtracting $\frac{2}{3}$ from both sides of the equation:

5x = \frac{7}{4} - \frac{2}{3}

Finding a Common Denominator

To subtract the fractions, we need to find a common denominator. The least common multiple of 4 and 3 is 12. We can rewrite the fractions with a common denominator:

5x = \frac{21}{12} - \frac{8}{12}

Subtracting the Fractions

Now that the fractions have a common denominator, we can subtract them:

5x = \frac{13}{12}

Multiplying Both Sides by 12

To eliminate the fraction, we can multiply both sides of the equation by 12:

60x = 13

Dividing Both Sides by 60

Finally, we can solve for $x$ by dividing both sides of the equation by 60:

x = \frac{13}{60}

Conclusion

In this article, we used mathematical equations to determine the correct representation of Leo's workout time. We set up an equation to represent the total time spent at the gym and solved for the variable $x$ . The final answer is $\frac{13}{60}$ hours, which represents the time spent on each weight machine.

Discussion

The equation we set up is a linear equation, and we solved for the variable $x$ using basic algebraic manipulations. This problem demonstrates the importance of understanding fractions and how to work with them in mathematical equations.

Real-World Applications

This problem has real-world applications in various fields, such as:

Fitness and Exercise: Understanding time and fractions is crucial for athletes and fitness enthusiasts who need to track their workout times and progress.
Business and Finance: Mathematical equations like the one we set up are used in business and finance to represent complex relationships between variables.
Science and Engineering: Fractions and mathematical equations are used in scientific and engineering applications to model real-world phenomena and make predictions.

Future Directions

In future articles, we can explore more complex mathematical equations and real-world applications. Some potential topics include:

Quadratic Equations: We can explore quadratic equations and their applications in various fields, such as physics and engineering.
Systems of Equations: We can discuss systems of equations and how to solve them using various methods, such as substitution and elimination.
Graphing and Functions: We can explore graphing and functions, including linear and quadratic functions, and their applications in real-world scenarios.

Conclusion

In conclusion, this article demonstrated the importance of mathematical equations in representing real-world scenarios. We set up an equation to represent Leo's workout time and solved for the variable $x$ . The final answer is $\frac{13}{60}$ hours, which represents the time spent on each weight machine. This problem has real-world applications in various fields, and we can explore more complex mathematical equations and real-world applications in future articles.

Introduction

In our previous article, we explored a real-life scenario involving time and fractions. Our protagonist, Leo, spent a significant amount of time working out at the gym, and we used mathematical equations to determine the correct representation of his workout time. In this article, we will answer some frequently asked questions (FAQs) related to the problem.

Q&A

Q: What is the total time spent on the weight machines?

A: The total time spent on the weight machines is $5x$ , where $x$ is the time spent on each machine.

Q: What is the time spent on the treadmill?

A: The time spent on the treadmill is $\frac{2}{3}$ of an hour.

Q: What is the total time spent at the gym?

A: The total time spent at the gym is $1 \frac{3}{4}$ hours, which is equivalent to $\frac{7}{4}$ hours.

Q: How do we set up the equation to represent the total time spent at the gym?

A: We set up the equation $5x + \frac{2}{3} = \frac{7}{4}$ to represent the total time spent at the gym.

Q: How do we solve for $x$ in the equation?

A: To solve for $x$ , we need to isolate the variable. We can start by subtracting $\frac{2}{3}$ from both sides of the equation, then find a common denominator, subtract the fractions, multiply both sides by 12, and finally divide both sides by 60.

Q: What is the final answer for $x$ ?

A: The final answer for $x$ is $\frac{13}{60}$ hours, which represents the time spent on each weight machine.

Q: What are some real-world applications of this problem?

A: This problem has real-world applications in various fields, such as fitness and exercise, business and finance, and science and engineering.

Q: Can we explore more complex mathematical equations and real-world applications in future articles?

A: Yes, we can explore more complex mathematical equations and real-world applications in future articles. Some potential topics include quadratic equations, systems of equations, and graphing and functions.

Conclusion

In this article, we answered some frequently asked questions related to the problem of Leo's gym workout time. We provided detailed explanations and examples to help readers understand the concepts and equations involved. We hope this article has been helpful in clarifying any doubts and providing a deeper understanding of the problem.

Discussion

The problem of Leo's gym workout time is a great example of how mathematical equations can be used to represent real-world scenarios. By setting up and solving an equation, we can gain a deeper understanding of the relationships between variables and make predictions about future outcomes.

Real-World Applications

This problem has real-world applications in various fields, such as fitness and exercise, business and finance, and science and engineering. By understanding mathematical equations and how to solve them, we can make informed decisions and predictions about complex systems.

Future Directions

In future articles, we can explore more complex mathematical equations and real-world applications. Some potential topics include:

Quadratic Equations: We can explore quadratic equations and their applications in various fields, such as physics and engineering.
Systems of Equations: We can discuss systems of equations and how to solve them using various methods, such as substitution and elimination.
Graphing and Functions: We can explore graphing and functions, including linear and quadratic functions, and their applications in real-world scenarios.

Conclusion

In conclusion, this article provided a Q&A section to help readers understand the problem of Leo's gym workout time. We hope this article has been helpful in clarifying any doubts and providing a deeper understanding of the problem. We look forward to exploring more complex mathematical equations and real-world applications in future articles.