50 ! micah can fill a box with books in 15 minutes. while micah fills the box, sydney takes the books out puts them on a shelf. with sydney taking books out of the box, it takes 20 minutes for micah to fill the box. which of the following can be used to determine the amount of time it takes for sydney to empty the box if micah is not adding books? a)1 over 15 plus 1 over 20 equals 1 over x b)1 over 20 minus 1 over x equals 1 over 15 c)1 over 15 minus 1 over x equals 1 over 20 d)1 over 15 minus 1 over x equals x over 20

Option C)1 over 15 minus 1 over x equals 1 over 20

Explanation:

Since, Micah can fill a box with books in 15 minutes.

Therefore, the work done by Micah in one minute= 1/15

Also, Sydney takes the books out puts them on a shelf.

And the times taken by Micah when Sydney is also taking the books outside from the self= 20 minutes

Therefore, the work done by Micah in one minute when Sydney  taking books out of the box= 1/20

Let Sydney alone takes x minutes to take books outsides the shelf.

Then, work done by Sydney in one minute=1/x

Thus, the work done by Sydney( by taking books out of the box)=  the work done by Micah - work done by Micah and Sydney simultaneously= 1/15-1/20

⇒1/x=1/15-1/20

⇒1/15-1/20=1/x

⇒1/15-1/x=1/20 is the required expression.

Therefore, Option C is correct.

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