Question

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?

Answer 1

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:

\[
3t - 2t = 12
\]

2. Simplify:

\[
t = 12
\]

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