Question

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 heroom 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:言十三中2=布Which value is a solution of the rational equation that must be discarded because of the context?

Answer 1

B) x = -10

Step-by-step explanation:

We were given that the equation is:

`\begin{gathered} (1)/(x)+(1)/(x+18)=(1)/(40) \\ \text{Taking the L.C.M. of the left side, we have:} \\ ((x+18))/(x(x+18))+(x)/(x(x+18))=(1)/(40) \\ ((x+18)+x)/(x(x+18))=(1)/(40) \\ (2x+18)/(x(x+18))=(1)/(40) \\ \text{Cross multiply, we have:} \\ x(x+18)=40\left(2x+18\right) \\ \text{Expanding the bracket, we have:} \\ x^2+18x=80x+720 \\ \text{Move the terms on the right side to the left side, we have:} \\ x^2+18x-80x-720=0 \\ x^2-62x-720=0 \\ \text{Factorising, we have:} \\ x^2-72x+10x-720=0 \\ \text{Factoring, we have:} \\ x(x-72)+10(x-72)=0 \\ (x-72)(x+10)=0 \\ x-72=0,x+10=0 \\ x=72,x=-10 \\ x=72(\text{the value of ''x'' cannot be negative because time cannot have a negative value}) \\ \\ \therefore x=-10\text{ is a solution of the equation that must be discarded} \end{gathered}`

x = -10 is a solution of the equation that must be discarded

Therefore, the correct option is B.