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)
You completed a total of 8.5 homework assignments, which means you fully completed 8 assignments and worked on half of another one.
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Convert 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 .
The number of assignments completed is 3 2 1 .
Explanation
Understanding the Problem We are given that it takes 1 2 1 hours to complete each homework assignment. We are also given that a total of 5 4 1 hours are spent on homework assignments. We want to find the number of assignments completed.
Converting to Improper Fractions First, convert the mixed numbers to improper fractions. We have 1 2 1 = 2 3 and 5 4 1 = 4 21 .
Defining Variables 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 .
Setting up the Equation The number of assignments completed is given by n = t T . Substitute the values of T and t into the equation: n = 2 3 4 21 .
Calculating the Number of Assignments Simplify the expression to find the value of n . n = 4 21 ⋅ 3 2 = 12 42 = 2 7 = 3.5
Final Answer Therefore, the number of assignments completed is 3.5 .
Examples
Understanding how to divide your time efficiently between tasks is a valuable skill. For instance, if you know it takes approximately 2 hours to prepare a presentation and you have a total of 7 hours available, you can calculate that you have time to prepare 3.5 presentations. This kind of calculation helps in planning and managing time effectively, whether it's for school projects, work assignments, or even planning a series of activities during a vacation.
