Answer: 30 days
Step-by-step explanation:
Working together, E & B get 1/45 of the job done per day
Working alone, C gets 1/x of the job done per day
Working together, E, B, & C get 1/18 of the job done per day.
[tex]EB:\dfrac{1}{45}\qquad C: \dfrac{1}{x}\qquad EBC:\dfrac{1}{18}\\\\\\\\EB+C=EBC\\\\ \dfrac{1}{45}\ +\dfrac{1}{x}=\dfrac{1}{18}\\\\\\(45\cdot 18\cdot x)\bigg(\dfrac{1}{45}+\dfrac{1}{x}=\dfrac{1}{18}\bigg)\\\\\\.\qquad \qquad 18x+810=45x\\\\.\qquad \qquad \qquad 810=27x\\\\.\qquad\qquad \qquad \large\boxed{30=x}[/tex]
