Perry can fill a sorter with oranges from the conveyer belt in 10 minutes. While Perry fills the sorter, Gillian takes oranges out of the sorter and puts them in shipping crates. With Gillian taking oranges out of the sorter, it takes 25 minutes for Perry to fill the sorter.

Which of the following can be used to determine the amount of time it takes for Gillian to empty the sorter if Perry does not add oranges?

A) 1 over 10 minus 1 over x equals 1 over 25
B) 1 over 10 minus 1 over 25 equals 1 over x
C) 1 over 25 minus 1 over x equals 1 over 10
D) 1 over 10 minus 1 over x equals x over 25

Step-by-step explanation: We are given to select the correct option that can be used to determine the amount of time it takes for Gillian to empty the sorter if Perry does not add oranges.

Let, 'x' minutes be the amount of time it takes for Gillian to empty the sorter if Perry does not add oranges.

We have

Time taken by Perry to fill the sorter with oranges from the conveyor belt

= 10 minutes.

So, in 1 min, the portion of the sorter filled by Perry from conveyor belt is

[tex]\dfrac{1}{10}.[/tex]

While Gillian taking oranges out of the sorter, time taken by Perry to fill the sorter with oranges = 25 minutes.

So, in 1 min, the portion of the sorter filled by Perry is

[tex]\dfrac{1}{25}.[/tex]

Time taken by Gillian to empty the sorter if Perry does not add oranges = x min.

So, in 1 minute, the portion of the sorter emptied by Gillian is given by

[tex]\dfrac{1}{x}.[/tex]

Therefore, the required equation that determine the amount of time it takes for Gillian to empty the sorter if Perry does not add oranges is given by

[tex]\dfrac{1}{10}-\dfrac{1}{x}=\dfrac{1}{25}.[/tex]

Thus, (A) is the correct option.