first up, lets review the assignments learning objectives
get familiar with this topic by reviewing instruction and answering a couple of questions.

question
devontre rode his bike uphill 5 miles and then back downhill. the rate at which devontre traveled downhill was 20 mph faster than his rate going uphill. if it took him 20 minutes longer to ride uphill than downhill, what was his uphill rate?

provide your answer below:

$r = $ mph

Question

first up, lets review the assignments learning objectives
get familiar with this topic by reviewing instruction and answering a couple of questions.

question
devontre rode his bike uphill 5 miles and then back downhill. the rate at which devontre traveled downhill was 20 mph faster than his rate going uphill. if it took him 20 minutes longer to ride uphill than downhill, what was his uphill rate?

provide your answer below:

$r = $   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" ], "new_concepts": [ "Distance Rate Time Problems" ], "current_concepts": [ "Solving Rational Equations", "Distance Rate Time Problems" ] } ## Set up the rational equation $$ \begin{aligned} &\text{Let } r \text{ be the uphill rate in mph. Downhill rate is } r + 20 \text{ mph.}\ &\text{Distance uphill } = 5 \text{ miles, Distance downhill } = 5 \text{ miles.}\ &\text{Time difference } = 20 \text{ minutes} = \frac{20}{60} \text{ hours} = \frac{1}{3} \text{ hours.}\ &\frac{5}{r} - \frac{5}{r + 20} = \frac{1}{3} \end{aligned} $$ ## Solve the equation for r $$ \begin{aligned} &3(r + 20) \cdot 5 - 3r \cdot 5 = r(r + 20)\ &15r + 300 - 15r = r^2 + 20r\ &r^2 + 20r - 300 = 0\ &(r + 30)(r - 10) = 0\ &r = 10 \quad (r > 0) \end{aligned} $$ $r =$ 10 mph { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Solving Rational Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Set up the rational equation

Solve the equation for r

Answer: