two cyclists, 60 miles apart, start riding toward each other at the same time. one cycles 2 times as fast as the other. if they meet 2 hours later, what is the speed (in mi/h) of the faster cyclist?

Question

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Algebraic Translation", "Linear Word Problems" ], "new_concepts": [ "Uniform Motion Problems" ], "current_concepts": [ "Algebraic Translation", "Linear Word Problems", "Uniform Motion Problems" ] } ## Define variables for the speeds Using the *Algebraic Translation* knowledge point Let $r$ be the speed of the slower cyclist in miles per hour (mi/h). The speed of the faster cyclist is $2r$. ## Set up the distance equation Using the *Linear Word Problems* knowledge point $$ \begin{aligned} \text{Distance} &= \text{Speed} \times \text{Time} \ d_1 + d_2 &= 60 \ r(2) + 2r(2) &= 60 \ 2r + 4r &= 60 \end{aligned} $$ ## Solve for the slower speed Using the *Linear Word Problems* knowledge point $$ \begin{aligned} 6r &= 60 \ r &= 10 \end{aligned} $$ ## Calculate the faster speed Using the *Algebraic Translation* knowledge point $$ \begin{aligned} \text{Speed of faster cyclist} &= 2r \ &= 2(10) \ &= 20 \end{aligned} $$ Two cyclists, 60 miles apart, start riding toward each other at the same time. One cycles 2 times as fast as the other. If they meet 2 hours later, what is the speed (in mi/h) of the faster cyclist? 20 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Linear Word Problems" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Define variables for the speeds

Set up the distance equation

Solve for the slower speed

Calculate the faster speed

Answer: