Question

Use the expressions to help you solve. After how many minutes will Tank A and Tank B have the same amount of water? Solve on paper, then enter your answer on Zearn.
Liters in Tank A after t minutes:
380+(−9t)
Liters in Tank B after t minutes:
420+(−13t)
Tank A and Tank B will have the same amount of water after
minutes.

Answer 1

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**.