Sierra has a bucket that originally contained 260 fl oz of water and is being filled at a rate of 5 fl oz per minute. Brian has a bucket that originally contained 650 fl oz of water and is being drained at a rate of 8 fl oz per minute. What is x, the number of minutes that need to pass in order for the two buckets to contain the same amount of water?
Sierra's bucket is being filled at a rate of 5 fl oz per minute, so after x minutes, it will contain 260 + 5x fl oz of water.
Brian's bucket is being drained at a rate of 8 fl oz per minute, so after x minutes, it will contain 650 - 8x fl oz of water.
Since the two buckets will contain the same amount of water after x minutes, we can set up the equation 260 + 5x = 650 - 8x.
Combining like terms, we get 13x = 390.
Dividing both sides by 13, we get x = 30. Answer: \boxed{30}.
To find the number of minutes (x) it takes for the two buckets to contain the same amount of water, we can set up an equation and solve for x.
Let's denote the amount of water in Sierra's bucket after x minutes as S(x) and the amount of water in Brian's bucket after x minutes as B(x).
Given:
Initial amount of water in Sierra's bucket = 260 fl oz
Rate of filling Sierra's bucket = 5 fl oz per minute
Initial amount of water in Brian's bucket = 650 fl oz
Rate of draining Brian's bucket = 8 fl oz per minute
We can write the equations:
S(x) = 260 + 5x
B(x) = 650 - 8x
To find when S(x) = B(x), we set the two equations equal to each other:
260 + 5x = 650 - 8x
Simplifying the equation:
13x = 390
x = 30
Therefore, it will take 30 minutes (x = 30) for the two buckets to contain the same amount of water.
To find the number of minutes that need to pass in order for the two buckets to contain the same amount of water, we need to set up an equation and solve for x.
Let's assume that after x minutes, Sierra's bucket contains y fl oz of water.
The rate at which Sierra's bucket is being filled is 5 fl oz per minute. So after x minutes, the amount of water in Sierra's bucket can be represented as: y = 260 + 5x.
Similarly, after x minutes, the amount of water in Brian's bucket can be represented as: 650 - 8x.
Since we want to find the value of x when the two buckets contain the same amount of water, we can set up the following equation and solve for x:
260 + 5x = 650 - 8x
Adding 8x to both sides of the equation:
8x + 5x + 260 = 650
Combining like terms:
13x + 260 = 650
Subtracting 260 from both sides of the equation:
13x = 650 - 260
Simplifying:
13x = 390
Dividing both sides of the equation by 13:
x = 390 / 13
Calculating:
x = 30
Therefore, the two buckets will contain the same amount of water after 30 minutes.