select all the correct answers.

for the first 80 miles of her road trip, lina travels 10 miles/hour slower than she did for the remaining 50 miles of her trip. if $s$ represents linas speed during the first part of her trip, which expressions represent the total time of her trip in hours?

$\frac{80}{s + 10} +
\frac{50}{s}$

$\frac{130}{s(s + 10)}$

$\frac{130s - 800}{s(s - 10)}$

$\frac{80}{s} + \frac{50}{s + 10}$

$\frac{130s + 800}{s(s + 10)}$

Question

select all the correct answers.

for the first 80 miles of her road trip, lina travels 10 miles/hour slower than she did for the remaining 50 miles of her trip. if $s$ represents linas speed during the first part of her trip, which expressions represent the total time of her trip in hours?

$\frac{80}{s + 10} +
\frac{50}{s}$

$\frac{130}{s(s + 10)}$

$\frac{130s - 800}{s(s - 10)}$

$\frac{80}{s} + \frac{50}{s + 10}$

$\frac{130s + 800}{s(s + 10)}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Rational Expression Addition", "Rational Expression Simplification" ], "new_concepts": [], "current_concepts": [ "Rational Expression Addition", "Rational Expression Simplification", "Work Rate Problems" ] } ## Formulate expressions for the time of each part of the trip $$ \begin{aligned} &\text{Speed during first part} = s\ &\text{Distance of first part} = 80\text{ miles}\ &\text{Time for first part} = \frac{80}{s}\ &\text{Speed during second part} = s + 10\ &\text{Distance of second part} = 50\text{ miles}\ &\text{Time for second part} = \frac{50}{s + 10}\ &\text{Total time} = \frac{80}{s} + \frac{50}{s + 10} \end{aligned} $$ ## Simplify the total time expression $$ \begin{aligned} \frac{80}{s} + \frac{50}{s + 10} &= \frac{80(s + 10) + 50s}{s(s + 10)}\ &= \frac{80s + 800 + 50s}{s(s + 10)}\ &= \frac{130s + 800}{s(s + 10)} \end{aligned} $$ ## Identify the matching options $$ \begin{aligned} &\text{Option 4: } \frac{80}{s} + \frac{50}{s + 10}\ &\text{Option 5: } \frac{130s + 800}{s(s + 10)} \end{aligned} $$

(A) $\frac{80}{s + 10} + \frac{50}{s}$

(B) $\frac{130}{s(s + 10)}$

(C) $\frac{130s - 800}{s(s - 10)}$

(D) $\frac{80}{s} + \frac{50}{s + 10}$

(E) $\frac{130s + 800}{s(s + 10)}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Rational Expression Addition" ] }

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QUESTION IMAGE

Question

Explanation:

Formulate expressions for the time of each part of the trip

Simplify the total time expression

Identify the matching options

Answer: