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?(1 point)
Let's represent the amount of time in minutes by "t" and the amount of liquid in the empty vat by "x."
Since the empty vat is filling at a rate of 6 gallons per minute, we can express the amount of liquid in the empty vat as 6t.
Since the other vat already contains 28 gallons and is filling at a rate of 4 gallons per minute, we can express the amount of liquid in the second vat as 28 + 4t.
The two vats will have the same amount of liquid when 6t = 28 + 4t.
Subtracting 4t from both sides, we get 2t = 28.
Finally, dividing both sides by 2, we find that 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 need to set up an equation based on the information given.
Let's assume after 't' minutes, both vats will have the same amount of liquid. At this point, the first vat will have 6t gallons of liquid, and the second vat will have 28 + 4t gallons of liquid.
Now, we can set up an equation to solve for 't':
6t = 28 + 4t
Subtract 4t from both sides to isolate the variables:
6t - 4t = 28
Simplifying the equation, we have:
2t = 28
Now we can solve for 't' by dividing both sides of the equation by 2:
t = 28/2
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 need to set up an equation based on the given information.
Let's assume that it will take x minutes for the two vats to have the same amount of liquid.
The empty 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 filling at a rate of 4 gallons per minute, so after x minutes, it will have 28 + 4x gallons of liquid.
Setting up the equation:
6x = 28 + 4x
Simplifying the equation:
6x - 4x = 28
2x = 28
Dividing both sides of the equation by 2:
x = 14
Therefore, it will take 14 minutes for the two vats to have the same amount of liquid.