Question

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)
They will have the same amount of liquid after minutes.

Answer 1

That’s wrong

Answer 2

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.
The second vat is already at 28 gallons and is being filled at a rate of 4 gallons per minute, so after x minutes it will have 28 + 4x gallons.
Setting the two equations equal to each other, we have:
6x = 28 + 4x
2x = 28
x = 14
Therefore, the two vats will have the same amount of liquid after 14 minutes. Answer: \boxed{14}.

Answer 3

I apologize for the incorrect answer. Let's try to solve the problem again.

Let t 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 t minutes it will have 6t gallons.
The second vat is already at 28 gallons and is being filled at a rate of 4 gallons per minute, so after t minutes it will have 28 + 4t gallons.
Setting the two equations equal to each other, we have:
6t = 28 + 4t
2t = 28
t = 14

Therefore, the two vats will have the same amount of liquid after 14 minutes. Answer: \boxed{14}.