To find out when Tank A and Tank B have the same amount of water, we need to set their equations equal to each other and solve for \( t \).
The amount of water in Tank A after \( t \) minutes is given by: \[ A(t) = 380 - 9t \]
The amount of water in Tank B after \( t \) minutes is given by: \[ B(t) = 420 - 13t \]
Setting the two expressions equal to each other: \[ 380 - 9t = 420 - 13t \]
Next, we'll solve for \( t \). Start by adding \( 13t \) to both sides: \[ 380 - 9t + 13t = 420 \] \[ 380 + 4t = 420 \]
Now, subtract 380 from both sides: \[ 4t = 420 - 380 \] \[ 4t = 40 \]
Now, divide both sides by 4: \[ t = \frac{40}{4} = 10 \]
Thus, Tank A and Tank B will have the same amount of water after 10 minutes.