wayne and winston are scuba diving and are ascending to the surface. the function $y = 30x - 105$ represents waynes elevation in feet in terms of the time in minutes he ascends. the table represents winstons elevation in feet in terms of the time in minutes he ascends. assume that wayne and winston both ascend at a constant rate.

$\begin{array}{|c|c|}\hline x & y \\\hline 0 & -100 \\\hline 3 & -16 \\\hline\end{array}$

which statements about this situation are true?

wayne ascends at a faster speed.
winston ascends at a faster speed.
wayne and winston ascend at the same speed.
wayne was deeper when he began ascending.
winston was deeper when he began ascending.

Question

wayne and winston are scuba diving and are ascending to the surface. the function $y = 30x - 105$ represents waynes elevation in feet in terms of the time in minutes he ascends. the table represents winstons elevation in feet in terms of the time in minutes he ascends. assume that wayne and winston both ascend at a constant rate.

$\begin{array}{|c|c|}\hline x & y \\\hline 0 & -100 \\\hline 3 & -16 \\\hline\end{array}$

which statements about this situation are true?

wayne ascends at a faster speed.
  winston ascends at a faster speed.
  wayne and winston ascend at the same speed.
  wayne was deeper when he began ascending.
  winston was deeper when he began ascending.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Comparing Linear Functions", "Rate of Change Analysis" ], "new_concepts": [], "current_concepts": [ "Comparing Linear Functions", "Rate of Change Analysis", "Linear Modeling" ] } ## Determine rates of ascent $$ \begin{aligned} &\text{Wayne's rate: } m_{\text{Wayne}} = 30\text{ ft/min}\ &\text{Winston's rate: } m_{\text{Winston}} = \frac{-16 - (-100)}{3 - 0} = \frac{84}{3} = 28\text{ ft/min}\ &30 > 28 \implies \text{Wayne ascends at a faster speed.} \end{aligned} $$ ## Determine initial depths $$ \begin{aligned} &\text{Wayne's initial elevation (at } x = 0\text{): } y = -105\text{ ft (depth of 105 ft)}\ &\text{Winston's initial elevation (at } x = 0\text{): } y = -100\text{ ft (depth of 100 ft)}\ &105 > 100 \implies \text{Wayne was deeper when he began ascending.} \end{aligned} $$

Wayne ascends at a faster speed.

Winston ascends at a faster speed.

Wayne and Winston ascend at the same speed.

Wayne was deeper when he began ascending.

Winston was deeper when he began ascending.

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Comparing Linear Functions" ] }

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Explanation:

Determine rates of ascent

Determine initial depths

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