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 x be the number of minutes it takes for the two vats to have the same amount of liquid.

At time x, the first vat will have 6x gallons of liquid and the second vat will have 28 + 4x gallons of liquid.

Setting the two expressions equal to each other:

6x = 28 + 4x
2x = 28
x = 14

So, it will take 14 minutes for the two vats to have the same amount of liquid.