two cyclists, 128 miles apart, start riding toward each other at the same time. one cycles 3 times as fast as the other. if they meet 4 hours later, what is the speed (in mi/h) of the faster cyclist?

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Uniform Motion Problems" ], "new_concepts": [], "current_concepts": [ "Uniform Motion Problems", "Algebraic Translation" ] } ## Define variables for the speeds Using the *Uniform Motion Problems* knowledge point $$ \begin{aligned} &\text{Let } r \text{ be the speed of the slower cyclist (in mi/h).}\ &\text{The speed of the faster cyclist is } 3r. \end{aligned} $$ ## Set up the distance equation Using the *Uniform Motion Problems* knowledge point $$ \begin{aligned} &\text{Distance} = \text{Rate} \times \text{Time}\ &4r + 4(3r) = 128\ &4r + 12r = 128\ &16r = 128 \end{aligned} $$ ## Solve for the speeds Using the *Uniform Motion Problems* knowledge point $$ \begin{aligned} &r = \frac{128}{16} = 8\text{ mi/h}\ &\text{Faster speed} = 3r = 3(8) = 24\text{ mi/h} \end{aligned} $$ Two cyclists, 128 miles apart, start riding toward each other at the same time. One cycles 3 times as fast as the other. If they meet 4 hours later, what is the speed (in mi/h) of the faster cyclist? 24 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Uniform Motion Problems" ] }

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Explanation:

Define variables for the speeds

Set up the distance equation

Solve for the speeds

Answer: