Respuesta :
Answer:
17 days.
Step-by-step explanation:
Let the company B takes x hours to clear the parcel of land alone.
Now, company A takes 2 hours longer time to clear the parcel of land than company B.
Therefore, company A will take (x + 2) hours to do the same job alone.
Now, Company A in one hour does [tex]\frac{1}{x + 2}[/tex] part of the job.
And Company B in one hour does [tex]\frac{1}{2}[/tex] part of the job.
So, working together for one hour they will do [tex](\frac{1}{x + 2} + \frac{1}{x}) = \frac{2x + 2}{x(x + 2)}[/tex] parts of the job.
Therefore, they will complete the job in [tex]\frac{x(x + 2)}{2x +2}[/tex] hours.
Hence, [tex]\frac{x(x + 2)}{2x +2} = 9[/tex] {Given}
⇒ x² + 2x = 18x + 18
⇒ x² - 16x - 18 = 0
Applying the Sridhar Acharya's formula,
[tex]x = \frac{-(- 16) + \sqrt{(-16)^{2} - 4(-18) } }{2}[/tex]
{Neglecting the negative root as x can not be negative}
⇒ x = 17 days (Answer)
