It takes $1 \frac{1}{2}$ hours to complete each homework assignment assigned to you. You spend $51 / 4$ hours working on homework assignments. How many assignments did you complete in this time?
Answer (2)
The student completed 8 homework assignments in the given time. This was found by dividing the total time spent on homework by the time it takes for each assignment. Therefore, the result is 8 complete assignments.
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Convert the mixed numbers to improper fractions: 1 2 1 = 2 3 and 5 4 1 = 4 21 .
Divide the total time spent by the time per assignment: n = 2 3 4 21 .
Simplify the expression: n = 4 21 ⋅ 3 2 = 2 7 = 3.5 .
State the final answer: 3.5 .
Explanation
Problem Analysis Let's analyze the problem. We know the time it takes to complete one homework assignment and the total time spent on homework assignments. We need to find out how many assignments were completed.
Converting to Improper Fractions First, convert the mixed numbers to improper fractions. The time to complete each assignment is 1 2 1 = 2 3 hours. The total time spent on assignments is 5 4 1 = 4 21 hours.
Setting up the Equation Let t be the time to complete each assignment and T be the total time spent on assignments. Let n be the number of assignments completed. We have t = 2 3 and T = 4 21 . The number of assignments completed is given by n = t T .
Solving for the Number of Assignments Substitute the values of T and t into the equation: n = 2 3 4 21 . Simplify the expression to find the value of n : n = 4 21 ⋅ 3 2 = 12 42 = 2 7 = 3.5 .
Final Answer Since we are looking for the number of assignments completed, the answer is 3.5 .
Examples
Understanding how to divide your time efficiently is a valuable skill. For example, if you know you have 10 hours to study for three different exams and each exam requires a different amount of time, you can use similar calculations to allocate your time effectively. If exam A requires 2.5 hours, exam B requires 3.75 hours, and exam C requires 3.75 hours, you can ensure you dedicate the right amount of time to each subject to maximize your study efficiency. This type of time management is crucial for academic success and can be applied to various real-life scenarios, such as project management and task scheduling.
