john spent 30 minutes developing an estimate for a job. the job itself took 5 hours, 30 minutes to complete. what is the ratio of the time spent on the job estimate to the total time, including the estimate, spent on this job?
submit answer as #:# or fraction.

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Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Unit Conversion in Ratios", "Ratio Simplification" ], "new_concepts": [], "current_concepts": [ "Unit Conversion in Ratios", "Ratio Simplification", "Ratio Representation" ] } ## Convert all times to minutes $$ \begin{aligned} T_{\text{estimate}} &= 30\text{ minutes} \ T_{\text{job}} &= 5\text{ hours } 30\text{ minutes} = 5 \times 60 + 30 = 330\text{ minutes} \ T_{\text{total}} &= T_{\text{estimate}} + T_{\text{job}} = 30 + 330 = 360\text{ minutes} \end{aligned} $$ ## Calculate and simplify the ratio $$ \begin{aligned} \text{Ratio} &= \frac{T_{\text{estimate}}}{T_{\text{total}}} = \frac{30}{360} \ \text{Ratio} &= \frac{1}{12} \end{aligned} $$ John spent 30 minutes developing an estimate for a job. The job itself took 5 hours, 30 minutes to complete. What is the ratio of the time spent on the job estimate to the total time, including the estimate, spent on this job? Submit answer as #:# or fraction. $\frac{1}{12}$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Ratio Representation" ] }

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Explanation:

Convert all times to minutes

Calculate and simplify the ratio

Answer: