select the correct answer.\nit takes greg and nikki a total of 40 minutes to paint a room if they work…

select the correct answer.\nit 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.\nwhen x represents the number of minutes it takes nikki to paint the room working alone, the situation is represented by this equation: $\frac{1}{x}+\frac{1}{x + 18}=\frac{1}{40}$.\nwhich value is a solution of the rational equation that must be discarded because of the context?\na. $x = 0$\nb. $x=-10$\nc. $x=-18$\nd. $x=-72$

select the correct answer.\nit 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.\nwhen x represents the number of minutes it takes nikki to paint the room working alone, the situation is represented by this equation: $\frac{1}{x}+\frac{1}{x + 18}=\frac{1}{40}$.\nwhich value is a solution of the rational equation that must be discarded because of the context?\na. $x = 0$\nb. $x=-10$\nc. $x=-18$\nd. $x=-72$

Answer

Explanation:

Step1: Analyze the context

The variable $x$ represents the number of minutes it takes Nikki to paint the room alone. Time cannot be negative in this real - world context.

Step2: Check each option

  • Option A: $x = 0$ would mean Nikki takes 0 minutes to paint the room alone, which is not possible in a real - world work - rate scenario. But we are looking for negative values to discard based on the context of time being non - negative.
  • Option B: $x=- 10$ is a negative value. Since $x$ represents time (in minutes) for Nikki to paint the room alone, a negative value for time does not make sense in this context.
  • Option C: $x = - 18$ is also negative, but $x$ represents Nikki's time alone and $x + 18$ represents Greg's time alone. If $x=-18$, Greg's time $x + 18=0$ which is not valid, but the more fundamental issue is with Nikki's time being negative.
  • Option D: $x=-72$ is negative, but the most straightforward negative value that represents Nikki's time and must be discarded due to the non - negativity of time for work is $x=-10$.

Answer:

B. $x = - 10$