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?
-1/10-1/x=1/25
-1/10+1/25=1/x*
-1/25-1/x=1/10
-1/10-1/x=x/25
Any and all help appreciated. Thank you!
ratePerry=1 belt/10 min
rateGillian=?
rate combined=1belt/25 min
Well, in 50 min, perry could fill 5 belts, and with gillian emptying, there are two belts left each 50 min. So gillian must be pulling out 3 belts /50 min
or 1belt/(50/3min)=1/(1belt/16.6min)
which tells us the belt could be emptied by Gillian in 16.6 min
Thank you! You were correct!
Let's analyze the information given step-by-step:
1. Perry takes 10 minutes to fill the sorter.
2. With Gillian taking oranges out of the sorter, it takes 25 minutes for Perry to fill the sorter.
Now, let's denote Gillian's time to empty the sorter as "x".
We can create the following equation based on the given information:
1/10 - 1/x = 1/25
Now, let's simplify this equation:
Multiply all terms by 10x to clear the fractions:
x - 10 = 2x/5
Multiply all terms by 5 to eliminate the remaining fractions:
5x - 50 = 2x
Rearrange the equation by moving 2x to the left side:
5x - 2x = 50
3x = 50
Divide both sides of the equation by 3:
x = 50/3
Therefore, the correct equation to determine the amount of time it takes for Gillian to empty the sorter if Perry does not add oranges is:
-1/10 - 1/x = 1/25
So, the correct answer is: -1/10 - 1/x = 1/25
To determine the amount of time it takes for Gillian to empty the sorter, we need to find the value of x in the equation.
Let's break down the problem using the given information:
We know that Perry can fill the sorter in 10 minutes.
So, in one minute, Perry can fill 1/10th of the sorter.
When Gillian is taking oranges out of the sorter, it takes Perry 25 minutes to fill the sorter.
So, in one minute, with Gillian taking oranges out of the sorter, Perry can fill 1/25th of the sorter.
Now, if Gillian is taking oranges out of the sorter without Perry adding oranges, we want to find out how long it takes her to empty the sorter completely.
Considering that Perry can fill 1/10th of the sorter in one minute and Gillian can take out 1/xth of the sorter in one minute, their combined work rate will be their individual rates added together. Since Gillian is taking oranges out, her rate will be negative.
So, the equation representing this scenario will be:
-1/10 + 1/x = 1/t
Here, t represents the amount of time it takes for Gillian to empty the sorter.
Therefore, the correct equation from the given options is:
-1/10 + 1/25 = 1/x*
Option -1/10+1/25=1/x is the correct choice.