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

17 days.

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
`(1)/(x + 2)` part of the job.

And Company B in one hour does
`(1)/(2)` part of the job.

So, working together for one hour they will do
`((1)/(x + 2) + (1)/(x)) = (2x + 2)/(x(x + 2))` parts of the job.

Therefore, they will complete the job in
`(x(x + 2))/(2x +2)` hours.

Hence,
`(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)