Consider the following scenario. Your gas tank holds 60 litres of fuel, and it is currently a quarter full. Then, you burn 1 over 2 of a litre per hour driven. Which formula represents the fuel remaining in the gas tank in terms of the number of hours driven?

Given the scenario:

- The gas tank holds 60 litres of fuel.
- It is currently a quarter full, so it has \( \frac{1}{4} \times 60 = 15 \) litres of fuel.
- You burn \( \frac{1}{2} \) litre per hour driven.

Let's define:
- \( t \) as the number of hours driven.
- \( f(t) \) as the fuel remaining in the tank after \( t \) hours.

The fuel consumed after \( t \) hours is \( \frac{1}{2} \times t \) litres.

Therefore, the formula for the fuel remaining in the tank after \( t \) hours is:

\[
f(t) = 15 - \frac{1}{2}t
\]

This formula shows the relationship between the fuel remaining in the tank and the number of hours driven.

Would you like a more detailed explanation or have any other questions?

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Here are 5 related questions for further practice:

1. How much fuel is left after driving for 10 hours?
2. What happens to the fuel remaining if you double the driving hours?
3. How many hours can you drive before the fuel runs out?
4. If you start with a half-full tank, what would the formula be?
5. What is the fuel remaining after 25 hours of driving?

**Tip:** Always double-check your initial conditions and rates when setting up a linear function to ensure your equation accurately represents the scenario.

Understand how to calculate the fuel remaining in a gas tank based on hours driven with a step-by-step mathematical formula. This problem involves linear equations and rates, suitable for Grades 7-9 students.

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