Question

Two companies working together can clear a parcel of land in 9 hours. Working alone, it would take company A 2 hours longer to clear the land than it would company B. How long would it take company B to clear the parcel of land alone?

Answer 1

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 $\frac{1}{x + 2}$ part of the job.

And Company B in one hour does $\frac{1}{2}$ part of the job.

So, working together for one hour they will do $(\frac{1}{x + 2} + \frac{1}{x}) = \frac{2x + 2}{x(x + 2)}$ parts of the job.

Therefore, they will complete the job in $\frac{x(x + 2)}{2x +2}$ hours.

Hence, $\frac{x(x + 2)}{2x +2} = 9$ {Given}

⇒ x² + 2x = 18x + 18

⇒ x² - 16x - 18 = 0

Applying the Sridhar Acharya's formula,  

$x = \frac{-(- 16) + \sqrt{(-16)^{2} - 4(-18) } }{2}$  

{Neglecting the negative root as x can not be negative}

⇒ x = 17 days (Answer)