Question

George filled up his car with gas before embarking on a road trip across the country. The capacity of George's gas tank is 12 gallons and her car uses 2 gallons of gas for every hour driven. Make a table of values and then write an equation for G, in terms of t, representing the number of gallons of gas remaining in George's gas tank after t hours of driving.

Answer 1

Given that the capacity of George's gas tank is 12 gallons and her car uses 2 gallons of gas for every hour driven.

`\begin{gathered} G_(\circ)=12 \\ m=-2 \end{gathered}`

slope m is negative since the gas is reducing every hour.

Writing the equation for G, in terms of t, representing the number of gallons of gas remaining in George's gas tank after t hours of driving.​

`\begin{gathered} G=G_(\circ)+mt \\ G=12+(-2)t \\ G=12-2t \end{gathered}`

The equation for G is;

`G=12-2t`

Calculating the number of gallons remaining in the tank after 0,1,2 and 3 hours, we have;

`\begin{gathered} G=12-2t \\ at\text{ t=0}; \\ G_0=12-2(0)=12 \\ at\text{ t=1}; \\ G_1=12-2(1)=10 \\ at\text{ t=2}; \\ G_{2_{}}=12-2(2)=12-4=8 \\ at\text{ t=3;} \\ G_3=12-2(3)=12-6=6 \end{gathered}`

Completing the table, we have;