question

josephine can correct her students test papers in 5 hours, but if her teachers assistant helps, it would take them 3 hours. how long would it take the assistant to do it alone?

provide your answer below:

$t =$ hour(s) and minutes

Question

question

josephine can correct her students test papers in 5 hours, but if her teachers assistant helps, it would take them 3 hours. how long would it take the assistant to do it alone?

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", "Solving Rational Equations" ], "new_concepts": [], "current_concepts": [ "Work Rate Problems", "Solving Rational Equations" ] } ## Set up the work rate equation $$ \frac{1}{5} + \frac{1}{t} = \frac{1}{3} $$ ## Solve for the unknown time $t$ $$ \begin{aligned} \frac{1}{t} &= \frac{1}{3} - \frac{1}{5} \ \frac{1}{t} &= \frac{5 - 3}{15} \ \frac{1}{t} &= \frac{2}{15} \ t &= \frac{15}{2} = 7.5 \text{ hours} \end{aligned} $$ ## Convert decimal hours to hours and minutes $$ \begin{aligned} 7.5 \text{ hours} &= 7 \text{ hours} + 0.5 \times 60 \text{ minutes} \ &= 7 \text{ hours and } 30 \text{ minutes} \end{aligned} $$ Josephine can correct her students' test papers in 5 hours, but if her teacher's assistant helps, it would take them 3 hours. How long would it take the assistant to do it alone? Provide your answer below: $t =$ 7 hour(s) and 30 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 unknown time \(t\)

Convert decimal hours to hours and minutes

Answer: