Consider the following scenario. Your gas tank holds 60 litres of fuel, and it is currently a quarter full. Then, you burn

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.

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

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

This formula represents the amount of fuel left in the tank as a function of the number of hours driven.

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

---

Here are 5 related questions for further practice:

1. If the tank was half full instead of a quarter, what would the formula for the fuel remaining be?
2. How long can you drive before the tank is empty?
3. How much fuel would remain after 10 hours of driving?
4. If the fuel consumption increased to \( \frac{3}{4} \) litres per hour, how would the formula change?
5. What would the graph of the function \( f(t) \) look like?

**Tip:** When working with word problems, identify all given information and variables before setting up the equation.

Learn how to calculate the amount of fuel remaining in a gas tank over time with a detailed step-by-step solution. Given a 60-litre tank a quarter full, burning half a litre per hour driven, understand the formula for fuel remaining in terms of hours driven. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation