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 minutes when will the two vats have the same amount of liquid. use x as a your variable

1 answer

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

The amount of liquid in the first vat after x minutes is 6x gallons.

The amount of liquid in the second vat after x minutes is 28 + 4x gallons.

To find when the two vats have the same amount of liquid, we set the two expressions equal to each other:

6x = 28 + 4x

Subtracting 4x from both sides, we get:

2x = 28

Dividing by 2, we find:

x = 14

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