question

mary can clean her apartment in 6 hours, while her roommate can clean the apartment in 5 hours. if they work together, how long would it take them to clean the apartment? round your answer to the nearest minute.

provide your answer below:

$t =$ hour(s) and minutes

Question

question

mary can clean her apartment in 6 hours, while her roommate can clean the apartment in 5 hours. if they work together, how long would it take them to clean the apartment? round your answer to the nearest minute.

provide your answer below:

$t =$   hour(s) and   minutes

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Work Rate Problems" ], "new_concepts": [], "current_concepts": [ "Work Rate Problems", "Solving Rational Equations" ] } ## Set up the work rate equation $$ \frac{1}{6} + \frac{1}{5} = \frac{1}{t} $$ ## Solve for the combined time in hours $$ \begin{aligned} \frac{5 + 6}{30} &= \frac{1}{t} \ \frac{11}{30} &= \frac{1}{t} \ t &= \frac{30}{11} \approx 2.7272\text{ hours} \end{aligned} $$ ## Convert the fractional part to minutes $$ \begin{aligned} \text{Hours} &= 2 \ \text{Minutes} &= \frac{8}{11} \times 60 = \frac{480}{11} \approx 43.636 \approx 44 \end{aligned} $$ Mary can clean her apartment in 6 hours, while her roommate can clean the apartment in 5 hours. If they work together, how long would it take them to clean the apartment? Round your answer to the nearest minute. Provide your answer below: $t =$ 2 hour(s) and 44 minutes { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Work Rate Problems" ] }

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QUESTION IMAGE

Question

Explanation:

Set up the work rate equation

Solve for the combined time in hours

Convert the fractional part to minutes

Answer: