dennis went cross-country skiing for 6 hours on saturday. he skied 20 miles uphill and then 20 miles back downhill, returning to his starting point. his uphill speed was 5 mph slower than his downhill speed. what was denniss speed going uphill and his speed going downhill?

provide your answer below:

uphill = mph, downhill = mph

Question

dennis went cross-country skiing for 6 hours on saturday. he skied 20 miles uphill and then 20 miles back downhill, returning to his starting point. his uphill speed was 5 mph slower than his downhill speed. what was denniss speed going uphill and his speed going downhill?

provide your answer below:

uphill = mph, downhill = mph

provide your answer below:

uphill =   mph, downhill =   mph

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Solving Rational Equations", "Solving Quadratic Equations" ], "new_concepts": [], "current_concepts": [ "Solving Rational Equations", "Solving Quadratic Equations", "Proportional Reasoning" ] } ## Set up the rational equation $$ \begin{aligned} &\text{Let } x = \text{uphill speed (mph)}\ &x + 5 = \text{downhill speed (mph)}\ &\frac{20}{x} + \frac{20}{x + 5} = 6 \end{aligned} $$ ## Solve the equation for x $$ \begin{aligned} &20(x + 5) + 20x = 6x(x + 5)\ &20x + 100 + 20x = 6x^2 + 30x\ &6x^2 - 10x - 100 = 0\ &3x^2 - 5x - 50 = 0\ &(3x + 10)(x - 5) = 0\ &x = 5 \quad (x > 0) \end{aligned} $$ ## Calculate speeds $$ \begin{aligned} &\text{uphill} = 5\text{ mph}\ &\text{downhill} = 5 + 5 = 10\text{ mph} \end{aligned} $$ uphill = 5 mph, downhill = 10 mph { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Solving Rational Equations" ] }

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Question

Explanation:

Set up the rational equation

Solve the equation for x

Calculate speeds

Answer: