Question
id. 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.
Answers
GPT-4o mini
Let \( t \) be the time in minutes after the start of the filling process.
The first vat is empty and filling at a rate of 6 gallons per minute, so the amount of liquid in the first vat after \( t \) minutes is:
\[
6t
\]
The second vat starts with 28 gallons and is filling at a rate of 4 gallons per minute, so the amount of liquid in the second vat after \( t \) minutes is:
\[
28 + 4t
\]
We want to find the time \( t \) when both vats contain the same amount of liquid:
\[
6t = 28 + 4t
\]
Now, we can solve for \( t \):
1. Subtract \( 4t \) from both sides:
\[
6t - 4t = 28
\]
\[
2t = 28
\]
2. Divide by 2:
\[
t = 14
\]
Therefore, the two vats will have the same amount of liquid after **14 minutes**.
The first vat is empty and filling at a rate of 6 gallons per minute, so the amount of liquid in the first vat after \( t \) minutes is:
\[
6t
\]
The second vat starts with 28 gallons and is filling at a rate of 4 gallons per minute, so the amount of liquid in the second vat after \( t \) minutes is:
\[
28 + 4t
\]
We want to find the time \( t \) when both vats contain the same amount of liquid:
\[
6t = 28 + 4t
\]
Now, we can solve for \( t \):
1. Subtract \( 4t \) from both sides:
\[
6t - 4t = 28
\]
\[
2t = 28
\]
2. Divide by 2:
\[
t = 14
\]
Therefore, the two vats will have the same amount of liquid after **14 minutes**.