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)

Answer 1

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.