Select the equation that goes with the word problem and answer the question:

Two fish tanks are being filled. The first tank is empty and is being filled at a rate of 3 gallons per minute, the second tank has 12 gallons in it and is being filled at 2 gallons per minute. How long will it take for the tanks to have the same amount of water?

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
2 hours ago

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 \( t \):

  1. Subtract \( 2t \) from both sides:

\[ 3t - 2t = 12 \]

  1. Simplify:

\[ t = 12 \]

Thus, it will take 12 minutes for the two tanks to have the same amount of water.