Question

Two pumps are filling large vats of liquid. One that 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? They will have the same amount of liquid after _ minutes.

Answer 1

Let's call the time it takes for the two vats to have the same amount of liquid "x" minutes.

After x minutes, the first vat will have filled 6x gallons (since it fills at a rate of 6 gallons per minute).

After x minutes, the second vat will have filled 28 + 4x gallons (since it already contains 28 gallons and fills at a rate of 4 gallons per minute).

Since we want the two vats to have the same amount of liquid, we can set up the following equation:

6x = 28 + 4x

Now we can solve for x:

6x - 4x = 28

2x = 28

x = 28/2

x = 14

Therefore, the two vats will have the same amount of liquid after 14 minutes.