Savannah filled up her car with gas before embarking on a road trip across the country. The car uses 1.25 gallons of gas for every hour driven and the capacity of the gas tank is 10 gallons. Write an equation for G, commaG, in terms of t, commat, representing the number of gallons of gas remaining in Savannah's gas tank after tt hours of driving 

To model the amount of gas \( G \) remaining in Savannah's gas tank after \( t \) hours of driving, we can approach the problem step by step:

1. **Rate of gas consumption:** The car consumes 1.25 gallons of gas per hour.
2. **Initial amount of gas in the tank:** The gas tank has a capacity of 10 gallons at the start.

### Equation for remaining gas:

The amount of gas remaining \( G \) after \( t \) hours of driving can be calculated by subtracting the total amount of gas consumed after \( t \) hours from the initial amount of gas in the tank. The gas consumed is the product of the rate of consumption (1.25 gallons/hour) and the time \( t \) (hours).

\[
G(t) = 10 - 1.25t
\]

### Explanation:
- \( G(t) \) represents the number of gallons of gas remaining after \( t \) hours.
- The initial amount of gas is 10 gallons.
- The term \( 1.25t \) represents the amount of gas used after driving for \( t \) hours.

### Domain:
Since the gas tank is 10 gallons and the car uses 1.25 gallons per hour, the tank will be empty after \( \frac{10}{1.25} = 8 \) hours. Thus, the domain of this function is \( 0 \leq t \leq 8 \).

Let me know if you'd like further details or have any questions.

### Related questions:
1. How long can Savannah drive before running out of gas?
2. What is the total distance she can cover if her car drives at a speed of 60 mph?
3. What happens to the equation if the gas consumption changes to 1.5 gallons per hour?
4. How would the equation change if Savannah initially fills only 8 gallons?
5. If Savannah refuels after 4 hours, how does that affect the equation?

### Tip:
Always check the domain of a function in practical scenarios, especially when dealing with resources like fuel, time, or money!

Savannah filled up her car with gas before embarking on a road trip across the country. The car uses 1.25 gallons of gas for every hour driven and the capacity of the gas tank is 10 gallons. Write an equation for G, in terms of t, representing the number of gallons of gas remaining in Savannah's gas tank after t hours of driving.

Explore how to model gas consumption with the linear equation G(t) = 10 - 1.25t, representing the remaining gas in Savannah's car tank after driving for t hours. Learn about rate of change and function representation, suitable for Grades 6-8 students.

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