select the correct answer.

it takes greg and nikki a total of 40 minutes to paint a room if they work together. if greg works alone, he takes 18 minutes longer to paint the room than nikki takes if she works alone.

when $x$ represents the number of minutes it takes nikki to paint the room working alone, the situation is represented by this equation:

\\frac{1}{x} + \frac{1}{x + 18} = \frac{1}{40}\

which value is a solution of the rational equation that must be discarded because of the context?

$x = 0$
$x = -10$
$x = -18$
$x = -72$

Question

select the correct answer.

it takes greg and nikki a total of 40 minutes to paint a room if they work together. if greg works alone, he takes 18 minutes longer to paint the room than nikki takes if she works alone.

when $x$ represents the number of minutes it takes nikki to paint the room working alone, the situation is represented by this equation:

\\frac{1}{x} + \frac{1}{x + 18} = \frac{1}{40}\

which value is a solution of the rational equation that must be discarded because of the context?

$x = 0$
$x = -10$
$x = -18$
$x = -72$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Rational Equations", "Work Rate Problems", "Viable Solutions in Context" ], "new_concepts": [], "current_concepts": [ "Rational Equations", "Work Rate Problems", "Viable Solutions in Context" ] } ## Set up and clear the fractions in the rational equation $$ \begin{aligned} &\frac{1}{x} + \frac{1}{x + 18} = \frac{1}{40}, \quad x eq 0, \quad x eq -18\ &40(x + 18) + 40x = x(x + 18)\ &40x + 720 + 40x = x^2 + 18x\ &80x + 720 = x^2 + 18x \end{aligned} $$ ## Solve the resulting quadratic equation $$ \begin{aligned} &x^2 - 62x - 720 = 0\ &(x - 72)(x + 10) = 0\ &x = 72 \quad \text{or} \quad x = -10 \end{aligned} $$ ## Identify the non-viable solution in context $$ \begin{aligned} &\text{Since } x \text{ represents time (minutes), } x > 0.\ &x = -10 \text{ must be discarded because time cannot be negative.} \end{aligned} $$

(A) $x = 0$

(B) $x = -10$

(C) $x = -18$

(D) $x = -72$

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

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QUESTION IMAGE

Question

Explanation:

Set up and clear the fractions in the rational equation

Solve the resulting quadratic equation

Identify the non-viable solution in context

Answer: