to collect data on the signal strengths in a neighborhood, tracy must drive from house to house and take readings. she has a graduate student, dave, to assist her. tracy figures it would take her 8 hours to complete the task working alone, and that it would take dave 12 hours if he completed the task by himself.

how long will it take tracy and dave to complete the task together?

6.0 hours
4.8 hours
7.2 hours
3.6 hours

Question

to collect data on the signal strengths in a neighborhood, tracy must drive from house to house and take readings. she has a graduate student, dave, to assist her. tracy figures it would take her 8 hours to complete the task working alone, and that it would take dave 12 hours if he completed the task by himself.

how long will it take tracy and dave to complete the task together?

6.0 hours
4.8 hours
7.2 hours
3.6 hours

how long will it take tracy and dave to complete the task together?

6.0 hours
4.8 hours
7.2 hours
3.6 hours

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Work Rate Problems" ], "new_concepts": [], "current_concepts": [ "Work Rate Problems", "Rational Equations" ] } ## Identify individual work rates Using the *Work Rate Problems* knowledge point $$ \begin{aligned} R_{\text{Tracy}} &= \frac{1}{8} \text{ task/hour} \ R_{\text{Dave}} &= \frac{1}{12} \text{ task/hour} \end{aligned} $$ ## Determine the combined work rate Using the *Work Rate Problems* knowledge point $$ \begin{aligned} R_{\text{together}} &= R_{\text{Tracy}} + R_{\text{Dave}} \ R_{\text{together}} &= \frac{1}{8} + \frac{1}{12} = \frac{3}{24} + \frac{2}{24} = \frac{5}{24} \text{ task/hour} \end{aligned} $$ ## Calculate the combined time Using the *Work Rate Problems* knowledge point $$ \begin{aligned} t_{\text{together}} &= \frac{1}{R_{\text{together}}} \ t_{\text{together}} &= \frac{24}{5} = 4.8 \text{ hours} \end{aligned} $$

(A) 6.0 hours

(B) 4.8 hours

(C) 7.2 hours

(D) 3.6 hours

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Work Rate Problems" ] }

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QUESTION IMAGE

Question

Explanation:

Identify individual work rates

Determine the combined work rate

Calculate the combined time

Answer: