Two pumps are filling large vats of liquid. One vat is empty, and the pump is filling it at a rate of 6 gallons per minute. The other vat already contains 28 gallons and is continuing to fill at a rate of 4 gallons per minute. When will the two vats have the same amount of liquid?
Let's assume that after t minutes, the two vats will have the same amount of liquid.
Let V be the amount of liquid in the first vat after t minutes, and let W be the amount of liquid in the second vat after t minutes.
The amount of liquid in the first vat after t minutes is given by:
V = 6t
The amount of liquid in the second vat after t minutes is given by:
W = 28 + 4t
To find when the two vats have the same amount of liquid, we need to solve the equation:
V = W
6t = 28 + 4t
2t = 28
t = 14
Therefore, the two vats will have the same amount of liquid after 14 minutes.
To find out when the two vats will have the same amount of liquid, we can use a simple approach.
Let's assume the time it takes for the two vats to have the same amount of liquid is "t" minutes.
In "t" minutes, the first vat will have a total amount of liquid of 6t gallons, while the second vat will have a total amount of liquid of 28 + 4t gallons.
Since we are looking for the time when the two vats have the same amount of liquid, we can set up the following equation:
6t = 28 + 4t
Simplifying the equation, we have:
6t - 4t = 28
2t = 28
Dividing both sides by 2, we get:
t = 14
Therefore, it will take 14 minutes for the two vats to have the same amount of liquid.
To find out when the two vats will have the same amount of liquid, we can set up an equation based on the information given.
Let x be the number of minutes it takes for the two vats to have the same amount of liquid.
The first vat is being filled at a rate of 6 gallons per minute, so after x minutes, it will have 6x gallons of liquid.
The second vat already contains 28 gallons and is being filled at a rate of 4 gallons per minute. After x minutes, it will have 28 + 4x gallons of liquid.
Setting up the equation:
6x = 28 + 4x
We can simplify the equation by subtracting 4x from both sides:
2x = 28
Finally, we can solve for x by dividing both sides by 2:
x = 28/2
x = 14
Therefore, it will take 14 minutes for the two vats to have the same amount of liquid.