Let \( t \) be the time in minutes.
For the first tank:
- Initially empty: 0 gallons
- Filling rate: 3 gallons per minute
- Amount of water after \( t \) minutes: \( 3t \)
For the second tank:
- Initially has: 12 gallons
- Filling rate: 2 gallons per minute
- Amount of water after \( t \) minutes: \( 12 + 2t \)
To find when the two tanks have the same amount of water, we can set the equations equal to each other:
\[ 3t = 12 + 2t \]
Now, let's solve for \( t \):
- Subtract \( 2t \) from both sides:
\[ 3t - 2t = 12 \]
- Simplify:
\[ t = 12 \]
Thus, it will take 12 minutes for the two tanks to have the same amount of water.