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

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**.