Calculating Marie's Work Hours A Detailed Breakdown Of Two Jobs

Understanding Marie's Work Schedule

In this article, we will delve into the mathematics of Marie's work hours across two jobs. The central problem revolves around calculating the total hours Marie dedicated to her jobs, considering her varying work schedule. Marie's work commitment totaled 40 hours across these two jobs, a significant dedication of her time. To dissect her work hours effectively, we need to analyze the specific hours she invested in the first job on different days of the week. On Monday, she spent 4 1/2 hours on the first job. Tuesday saw her contribute 3 7/8 hours. Wednesday presented a consistent 5-hour commitment, and the same was true for Thursday. This detailed breakdown is crucial for accurately determining her total hours on the first job. Once we have this figure, we can subtract it from her total work hours of 40 to find out how much time she spent on the second job. This problem is a practical application of arithmetic, fractions, and time management, providing a real-world scenario where mathematical skills are essential. The ability to calculate and manage time effectively is a valuable asset in both personal and professional settings, highlighting the relevance of this exercise. By carefully adding up the fractions and whole numbers representing Marie's work hours, we can gain a clear understanding of her work distribution across the week.

Breaking Down the Hours on the First Job

Let's start by calculating Marie's total hours on her first job. To accurately determine the hours Marie dedicated to her first job, we need to sum the hours she worked on Monday, Tuesday, Wednesday, and Thursday. On Monday, Marie worked 4 1/2 hours, which is a mixed number. To make calculations easier, we can convert this to an improper fraction. Multiplying the whole number 4 by the denominator 2 gives us 8, and adding the numerator 1 results in 9. So, 4 1/2 hours is equivalent to 9/2 hours. On Tuesday, Marie worked 3 7/8 hours. Again, we convert this mixed number to an improper fraction. Multiplying 3 by 8 gives us 24, and adding 7 results in 31. Thus, 3 7/8 hours is equivalent to 31/8 hours. On Wednesday and Thursday, Marie worked 5 hours each day, totaling 10 hours for these two days. Now, we have the following figures: 9/2 hours on Monday, 31/8 hours on Tuesday, and 10 hours on Wednesday and Thursday combined. To add these values together, we need a common denominator for the fractions. The least common multiple of 2 and 8 is 8. So, we convert 9/2 to an equivalent fraction with a denominator of 8. Multiplying both the numerator and denominator of 9/2 by 4 gives us 36/8. Now we can add the fractions: 36/8 + 31/8. Adding the numerators, we get 67/8 hours for Monday and Tuesday combined. Next, we add the 10 hours from Wednesday and Thursday. To do this, we can express 10 as a fraction with a denominator of 8, which is 80/8. Now we add 67/8 and 80/8, resulting in 147/8 hours. This is the total time Marie spent on her first job. We can convert this improper fraction back to a mixed number to better understand the time in hours and minutes. Dividing 147 by 8, we get 18 with a remainder of 3. So, 147/8 hours is equal to 18 3/8 hours. This detailed calculation provides a clear picture of Marie's commitment to her first job, setting the stage for determining the time spent on her second job.

Calculating Hours on the Second Job

Now that we've accurately calculated the total time Marie spent on her first job, the next crucial step is to determine the number of hours she dedicated to her second job. To find this, we'll use a simple subtraction method, leveraging the information we already have. We know that Marie worked a total of 40 hours across both jobs. We've also determined that she spent 18 3/8 hours on her first job. Therefore, to find the hours spent on the second job, we need to subtract 18 3/8 from 40. This calculation will provide us with a clear understanding of Marie's time allocation between her two work commitments. Subtraction involving mixed numbers and whole numbers requires careful attention to detail, particularly when dealing with fractions. Let's break down the process step by step to ensure accuracy in our final answer. This step is essential for completing the overall picture of Marie's work schedule and provides valuable insights into her time management practices. The ability to subtract mixed numbers from whole numbers is a fundamental arithmetic skill, applicable in various real-world scenarios beyond just calculating work hours.

Step-by-Step Subtraction

To subtract 18 3/8 hours from 40 hours, we first need to rewrite 40 as a mixed number so that we can subtract the fractional part. We can do this by borrowing 1 from 40, making it 39, and expressing that 1 as 8/8. So, 40 becomes 39 8/8. Now, we can subtract 18 3/8 from 39 8/8. Subtracting the whole numbers, we have 39 - 18, which equals 21. Next, we subtract the fractions: 8/8 - 3/8. Subtracting the numerators, we get 5/8. So, the result of the subtraction is 21 5/8 hours. This means Marie worked 21 5/8 hours on her second job. To further understand this time, we can convert the fraction 5/8 to minutes. Since there are 60 minutes in an hour, we multiply 5/8 by 60. (5/8) * 60 = 300/8. Dividing 300 by 8, we get 37.5 minutes. Therefore, Marie worked 21 hours and 37.5 minutes on her second job. This detailed calculation provides a clear picture of Marie's time commitment to her second job, complementing our earlier analysis of her first job. This comprehensive understanding of her work schedule is a testament to the power of arithmetic in real-life applications.

Summary of Marie's Work Hours

In summary, we've successfully dissected Marie's work schedule across her two jobs, employing a combination of arithmetic operations including addition, subtraction, and fraction manipulation. Our analysis began with a detailed breakdown of the hours Marie dedicated to her first job. We converted mixed numbers to improper fractions, found common denominators, and carefully added the hours worked on Monday, Tuesday, Wednesday, and Thursday. This process revealed that Marie spent a total of 18 3/8 hours on her first job. Following this, we shifted our focus to calculating the hours Marie worked on her second job. Utilizing the information that she worked a total of 40 hours across both jobs, we subtracted the hours spent on the first job from the total hours. This subtraction involved rewriting the whole number as a mixed number to facilitate the subtraction of fractions. The result of this calculation showed that Marie dedicated 21 5/8 hours to her second job. To provide a more granular understanding of this time, we converted the fractional part of the hours into minutes, determining that Marie worked 21 hours and 37.5 minutes on her second job. Throughout this exercise, we've highlighted the practical application of mathematical concepts in real-world scenarios. The ability to accurately calculate and manage time is a valuable skill, applicable in both personal and professional contexts. Marie's work schedule serves as a compelling example of how arithmetic and fraction manipulation can be used to understand and optimize time allocation. This comprehensive analysis not only provides a clear picture of Marie's work hours but also underscores the importance of mathematical literacy in everyday life. By carefully breaking down the problem into manageable steps, we've demonstrated how complex calculations can be simplified and solved with precision.

Keywords Analysis

Understanding the Original Problem Statement

The original problem statement presents a scenario involving Marie's work hours across two jobs. The core of the problem lies in calculating and understanding how Marie allocates her time between these jobs. To fully grasp the problem, we need to dissect the information provided and identify the key components. The statement indicates that Marie worked a total of 40 hours across both jobs. This is a crucial piece of information as it sets the overall context for our calculations. It also specifies the hours Marie worked on her first job on particular days: 4 1/2 hours on Monday, 3 7/8 hours on Tuesday, and 5 hours each on Wednesday and Thursday. These figures provide the detailed data necessary for calculating the total hours Marie spent on her first job. The implicit question is to determine how many hours Marie worked on the second job. This requires us to first calculate the total hours spent on the first job and then subtract that figure from the overall total of 40 hours. The problem involves a blend of whole numbers and fractions, requiring us to be adept at converting between mixed numbers and improper fractions, as well as performing addition and subtraction with fractions. Understanding the nuances of the problem statement is paramount to developing an effective solution strategy. It involves not just identifying the numerical values but also recognizing the relationships between them and the ultimate goal of the calculation. By carefully analyzing the problem statement, we can break it down into smaller, more manageable parts, making the solution process more straightforward and accurate. This thorough understanding is the foundation for a successful resolution.

Repair Input Keyword

To repair and clarify the input keyword, we can rephrase the question to be more explicit and easier to understand. The original keyword, "Marie worked 40 total hours on two jobs. She worked 4 1/2 hours on the first job on Monday, 3 7/8 hours on Tuesday, 5 hours each on Wednesday and Thursday," can be refined to clearly ask the central question. A more direct and understandable question would be: "If Marie worked a total of 40 hours across two jobs, and she worked 4 1/2 hours on the first job on Monday, 3 7/8 hours on Tuesday, and 5 hours each on Wednesday and Thursday, how many hours did she work on the second job?" This revised question explicitly asks for the hours worked on the second job, making the problem's objective immediately clear. It also retains all the essential information from the original statement, ensuring that the context is preserved. The addition of "If" at the beginning sets the stage for a hypothetical scenario, while the phrase "how many hours did she work on the second job?" directly targets the desired outcome. This type of refinement is crucial in problem-solving, as a clear understanding of the question is the first step towards finding an accurate solution. By rephrasing the question, we eliminate any ambiguity and ensure that anyone attempting to solve the problem knows exactly what is being asked. This clarity is particularly important in mathematical problems, where precision and accuracy are paramount. The revised question serves as a solid foundation for the subsequent steps in the problem-solving process.