a boat has a speed of 9 miles per hour in calm water. it takes the boat 4 hours to travel upstream but only 2 hours to travel the same distance downstream. which equation can be used to find c, the speed of the current in miles per hour?

$2(9 - c) = 4(9 + c)$
$9 + c = 4(9 - c)$
$9 - c = 2(9 + c)$
$4(9 - c) = 2(9 + c)$

Question

a boat has a speed of 9 miles per hour in calm water. it takes the boat 4 hours to travel upstream but only 2 hours to travel the same distance downstream. which equation can be used to find c, the speed of the current in miles per hour?

\$2(9 - c) = 4(9 + c)\$
\$9 + c = 4(9 - c)\$
\$9 - c = 2(9 + c)\$
\$4(9 - c) = 2(9 + c)\$

$2(9 - c) = 4(9 + c)$
$9 + c = 4(9 - c)$
$9 - c = 2(9 + c)$
$4(9 - c) = 2(9 + c)$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Upstream and Downstream Motion" ], "new_concepts": [], "current_concepts": [ "Upstream and Downstream Motion", "Linear Equation Formulation" ] } ## Express upstream and downstream speeds $$ \begin{aligned} v_{\text{upstream}} &= 9 - c \ v_{\text{downstream}} &= 9 + c \end{aligned} $$ ## Formulate distance equations $$ \begin{aligned} d_{\text{upstream}} &= 4(9 - c) \ d_{\text{downstream}} &= 2(9 + c) \end{aligned} $$ ## Equate the distances $$ 4(9 - c) = 2(9 + c) $$

(A) $2(9 - c) = 4(9 + c)$

(B) $9 + c = 4(9 - c)$

(C) $9 - c = 2(9 + c)$

(D) $4(9 - c) = 2(9 + c)$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Linear Equation Formulation" ] }

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QUESTION IMAGE

Question

Explanation:

Express upstream and downstream speeds

Formulate distance equations

Equate the distances

Answer: