Question

Use the table to estimate. About when will the two tanks have the same amount of water? In other words, after about how many minutes will the liters in Tank A be equal to the liters in Tank B?
Tank A
Liters in Tank A after t minutes: 400+(−3t)
Tank B
Liters in Tank B after t minutes: 180+5t

Minutes Liters in Tank A Liters in Tank B
0 400 180
10 370 230
20 340 280
30 310 330

Between 10 and 20 minutes

Between 20 and 30 minutes

Answer 1

To determine when the two tanks will have the same amount of water, we need to set the equations for Tank A and Tank B equal to each other.

**Equations:**
- Tank A: \( A(t) = 400 - 3t \)
- Tank B: \( B(t) = 180 + 5t \)

We want to find \( t \) such that \( A(t) = B(t) \):

\[
400 - 3t = 180 + 5t
\]

Now, let's rearrange the equation:

1. Add \( 3t \) to both sides:
\[
400 = 180 + 5t + 3t
\]
\[
400 = 180 + 8t
\]

2. Subtract 180 from both sides:
\[
400 - 180 = 8t
\]
\[
220 = 8t
\]

3. Divide by 8:
\[
t = \frac{220}{8} = 27.5 \text{ minutes}
\]

Now, we know that \( t \approx 27.5 \) minutes.

Next, we should confirm that this estimation falls between the intervals given (10-20 minutes and 20-30 minutes).

- The intervals we have from the table are:
- At \( t = 20 \) minutes: Tank A has 340 liters and Tank B has 280 liters.
- At \( t = 30 \) minutes: Tank A has 310 liters and Tank B has 330 liters.

Since 27.5 minutes is between 20 and 30 minutes, the two tanks will have the same amount of water after about **27.5 minutes**.