Math Problem Statement

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.

Solution

To model the number of gallons of gas remaining in Savannah's gas tank after driving for tt hours, let's break down the information:

  • The car uses 1.25 gallons of gas per hour.
  • The capacity of the gas tank is 10 gallons.

The amount of gas used after tt hours is 1.25t1.25t gallons. Since the tank starts with 10 gallons, the number of gallons remaining after tt hours of driving, denoted by G(t)G(t), is the initial amount of gas minus the amount used:

G(t)=101.25tG(t) = 10 - 1.25t

This equation represents the number of gallons GG of gas left after driving for tt hours.

Would you like further details or have any questions?

Here are some related questions to explore further:

  1. How many hours can Savannah drive before the gas tank is empty?
  2. How much gas is left after driving for 4 hours?
  3. What happens to the gas remaining if Savannah drives for 8 hours?
  4. If Savannah starts with half a tank, how would the equation change?
  5. How many miles can Savannah drive if her car averages 20 miles per gallon?

Tip: Always check the units in word problems to ensure consistency when setting up equations.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations

Formulas

G(t) = 10 - 1.25t

Theorems

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Suitable Grade Level

Grades 6-8