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)

Question

They will have the same amount of liquid after
minutes.

Answer 1

Let \( t \) represent the time in minutes. We can set up equations for the amount of liquid in each vat over time.

For the first vat (starting empty and filling at 6 gallons per minute): \[ \text{Amount in vat 1 at time } t = 6t \]

For the second vat (starting with 28 gallons and filling at 4 gallons per minute): \[ \text{Amount in vat 2 at time } t = 28 + 4t \]

We want to find the time \( t \) when both vats have the same amount of liquid: \[ 6t = 28 + 4t \]

To solve for \( t \), we first subtract \( 4t \) from both sides: \[ 6t - 4t = 28 \] \[ 2t = 28 \]

Now, divide both sides by 2: \[ t = 14 \]

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