The Teamwork ChallengeThis activity directly aligns with the module's objective to "apply rational equations. to real-world scenarios,"' specifically focusing on work-rate problems which are a classic applicationleading to rational equations.Scenario: Imagine you are managing a small publishing house, and you have two proofreaders,Maria and Juan, They are both excellent at their job, but they work at different speeds. Youneed to estimate how long it will take them to proofread a new manuscript if they worktogether.Task:Individual Work Rates:Maria can proofread an entire manuscript by herself in 6 days◦Juan can proofread the same manuscript by himself in 4 days.2.Formulate the Rational Equation:◦ Think about what fraction of the manuscript each person completes in one day.Let T be the total time (in days) it takes for Maria and Juan to proofread themanuscript together.○ Set up a rational equation that represents the combined work rate of Maria andJuan working together to complete one whole manuscript.3.Solve the Equation:Solve the rational equation you formulated to find the value of T.4.Interpret the Result:Clearly explain what your calculated value of T means in the context of Maria and◦Juan proofreading the manuscript together. How many days willit take them?Expected Outcome: Students will submit their steps for formulating and solving the rationalequation, along with their interpretation of the answer.Simplified Assessment Criteria:Equation Formulation (40%): Correctly sets up the rational equation representing thecombined work rate.Equation Solving (40%): Accurately solves the rational equation, showing all necessarysteps..Interpretation (20%): Clearly explains the meaning of the solution in the context of theproblem.
Answer (1)
Individual ratesMaria: 1 manuscript in 6 days → rate = 1/6 per dayJuan: 1 manuscript in 4 days → rate = 1/4 per daySet up the rational equationLet T = time (in days) working together.Combined rate = 1/T.Equation: 1/T = 1/6 + 1/4SolveFind sum: 1/6 + 1/4 = 2/12 + 3/12 = 5/12So 1/T = 5/12 → T = 12/5 = 2.4 daysInterpretationWorking together, Maria and Juan finish in 2.4 days, which is 2 days, 9 hours, 36 minutes (0.4 day × 24 hours = 9.6 hours).
