stu trained for a triathlon for 5 hours yesterday. he ran 5 miles and then biked 80 miles. his biking speed is 15 mph faster than his running speed. what is his running speed?

provide your answer below:

$s = $ mph

Question

stu trained for a triathlon for 5 hours yesterday. he ran 5 miles and then biked 80 miles. his biking speed is 15 mph faster than his running speed. what is his running speed?

provide your answer below:

$s = $   mph

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Distance Rate Time Problems", "Solving Rational Equations" ], "new_concepts": [], "current_concepts": [ "Distance Rate Time Problems", "Solving Rational Equations" ] } ## Set up the rational equation $$ \begin{aligned} &\text{Let } s = \text{running speed (mph)}\ &\text{Biking speed} = s + 15\ &\text{Total time} = \frac{\text{Running distance}}{\text{Running speed}} + \frac{\text{Biking distance}}{\text{Biking speed}} = 5\ &\frac{5}{s} + \frac{80}{s + 15} = 5 \end{aligned} $$ ## Solve the equation for s $$ \begin{aligned} &\frac{1}{s} + \frac{16}{s + 15} = 1\ &(s + 15) + 16s = s(s + 15)\ &17s + 15 = s^2 + 15s\ &s^2 - 2s - 15 = 0\ &(s - 5)(s + 3) = 0 \end{aligned} $$ ## Determine the valid physical solution $$ \begin{aligned} &s = 5 \quad (\text{since } s > 0) \end{aligned} $$ Stu trained for a triathlon for 5 hours yesterday. He ran 5 miles and then biked 80 miles. His biking speed is 15 mph faster than his running speed. What is his running speed? Provide your answer below: $s =$ 5 mph { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Distance Rate Time Problems" ] }

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QUESTION IMAGE

Question

Explanation:

Set up the rational equation

Solve the equation for s

Determine the valid physical solution

Answer: