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Problem Summary:

• A 600-gallon tank is being drained at a rate of 60 gallons per minute.
• The goal is to complete four parts of the problem using this information:

Part (a) - Write a formula for W(t) (the number of gallons after t minutes):

The initial amount of water in the tank is 600 gallons, and water is draining at 60 gallons per minute.

This gives the equation for W(t) as: $W(t) = 600 - 60t$ Where:

• $W(t)$ is the amount of water in the tank after $t$ minutes,
• $600$ is the initial amount of water,
• $60t$ is the rate of water drained (gallons per minute times time).

Part (b) - How much water is in the tank after 3 minutes?

Substitute $t = 3$ into the equation from part (a): $W(3) = 600 - 60(3) = 600 - 180 = 420 \text{ gallons}$ So, after 3 minutes, 420 gallons remain in the tank.

Part (c) - Identify and interpret the graph:

We need to interpret the graph of $W(t) = 600 - 60t$. The correct graph will:

• Start at $t = 0$, with $W(0) = 600$ gallons (the y-intercept is at (0,600)),
• Decrease linearly (since the tank is being drained),
• Reach 0 gallons after $t = 10$ minutes (when the tank is empty).

Among the provided options, graph D best matches this behavior:

• It starts at 600 on the vertical axis,
• It has a negative slope, showing water being drained over time,
• It crosses the horizontal axis (W = 0) at around 10 minutes.

Part (d) - Identify intercepts:

• Y-intercept: The graph starts at 600 gallons when $t = 0$, so the y-intercept is $W(0) = 600$.
• X-intercept: The tank becomes empty after 10 minutes, so the x-intercept is $t = 10$.

This means the tank is drained after 10 minutes.

Do you want more details on any specific part or have further questions?

Here are 5 related questions to deepen your understanding:

1. What happens to the equation if the drainage rate changes?
2. How would the graph look if the tank were filled at a constant rate instead of drained?
3. Can you explain why the slope of the graph is negative?
4. What would the intercepts be if the initial water level was 800 gallons instead of 600?
5. How can you determine the time when the tank is half empty?

Tip: In a word problem involving rates of change, the slope of the line represents the rate (drainage or filling), while the y-intercept represents the starting value (initial quantity).