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Let's work through this problem step by step.

### Part (a)
We are asked to write a linear function \( W(t) \) that gives the number of gallons of water left in the tank after \( t \) minutes. 

The problem states:
- The tank is initially full with 300 gallons.
- Water is being drained at a rate of 30 gallons per minute.

The general formula for a linear function is \( W(t) = \text{{initial amount}} - (\text{{rate of change}}) \times t \). Here:
- The initial amount of water is 300 gallons.
- The rate of drainage is 30 gallons per minute (since the water is being drained, the rate is negative).

Thus, the linear function becomes:
\[
W(t) = 300 - 30t
\]

### Part (b)
Now, we need to find how much water is in the tank after 3 minutes. To do this, substitute \( t = 3 \) into the equation from part (a):

\[
W(3) = 300 - 30(3) = 300 - 90 = 210
\]

After 3 minutes, the tank contains **210 gallons** of water.

Would you like any more details on this solution? Here are some related questions to further explore this concept:

1. What would the linear function look like if the tank were being drained at 40 gallons per minute instead of 30?
2. How many minutes will it take for the tank to be completely empty?
3. What is the significance of the slope in this context?
4. How would the function change if the tank had started with 500 gallons instead of 300 gallons?
5. Could we model the situation if water were being added to the tank instead of being drained?

**Tip:** When dealing with linear functions in word problems, always identify the initial value (y-intercept) and the rate of change (slope) from the context provided.

A 300-gallon tank is initially full of water and is being drained at a rate of 30 gallons per minute. Complete parts (a) through (b).

Learn how to solve a linear function problem involving a 300-gallon tank that is being drained at 30 gallons per minute. This problem demonstrates how to set up and solve a linear equation to find the amount of water remaining after a certain time. Suitable for students in Grades 7-9.

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