a boat has a speed of 15 mph in calm water. it takes the boat 3 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?

3(15 - c) = 2(15 + c)
2(15 - c) = 3(15 + c)
15 - c = 15 + c
15 - 3c = 15 + 2c

Question

a boat has a speed of 15 mph in calm water. it takes the boat 3 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?

3(15 - c) = 2(15 + c)
2(15 - c) = 3(15 + c)
15 - c = 15 + c
15 - 3c = 15 + 2c

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Linear Equation Formulation" ], "new_concepts": [ "Upstream and Downstream Motion" ], "current_concepts": [ "Linear Equation Formulation", "Upstream and Downstream Motion" ] } ## Express upstream and downstream speeds $$ \begin{aligned} v_{\text{upstream}} &= 15 - c \ v_{\text{downstream}} &= 15 + c \end{aligned} $$ ## Formulate distance equations $$ \begin{aligned} d_{\text{upstream}} &= 3(15 - c) \ d_{\text{downstream}} &= 2(15 + c) \end{aligned} $$ ## Equate the distances $$ 3(15 - c) = 2(15 + c) $$

(A) 3(15 - c) = 2(15 + c)

(B) 2(15 - c) = 3(15 + c)

(C) 15 - c = 15 + c

(D) 15 - 3c = 15 + 2c

{ "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: