Question

1. A car has a 16-gallon fuel tank. When driven on a highway, it has a gasmileage of 30 miles per gallon. The gas mileage (also called "fuel efficiency")tells us the number of miles the car can travel for a particular amount of fuel(one gallon of gasoline, in this case). After filling the gas tank, the driver got ona highway and drove for a while.

Answer 1

Given:

Capacity of the car's fuel tank = 16 gallons

Gas mileage of car = 30 miles per gallon

Given that the driver filled the tank and got on a highway, let's solve for the following:

• (a) How many miles has the car traveled if it has the following amounts of gas left in the tank:

Use the expression:

$(16-g)\times30$

Where g reresents the amount of gas left.

• 15 gallons:

If the car has 15 gallons left, to calculate the distance traveled, we have:

$\begin{gathered} (16-15)\times30 \\ \\ =(1)\times30 \\ \\ =30\text{ miles} \end{gathered}$

If the car has 15 gallons left, it has traveled for 30 miles.

• 10 gallons:

For 10 gallons, we have:

$\begin{gathered} (16-10)\times30 \\ \\ =(6)\times30 \\ \\ =180\text{ miles} \end{gathered}$

If the car has 10 gallons left, it has traveled for 180 miles.

• 2.5 gallons:

$\begin{gathered} (16-2.5)\times180 \\ \\ =13.5\times180 \\ \\ =405\text{ miles} \end{gathered}$

If the car has 2.5 gallons left, it has traveled for 405 miles.

• Part b.

Let's write an equation that shows the relationship between the distance traveled (d), and the amount of gas left in the tank in gallons(x).

To write the equation, we have:

$d=(16-x)30$

• Part C.

Let's find the amount of gallons left in the tank when the car has traveled the following distances:

• 90 miles:

$\begin{gathered} x=16-\frac{90}{30} \\ \\ x=16-3 \\ \\ x=13\text{ gallons} \end{gathered}$

If the car has traveled 90 miles, it will have 13 gallons left in the tank.

• 246 miles:

$\begin{gathered} x=16-\frac{246}{30} \\ \\ x=16-8.2 \\ \\ x=7.8\text{ gallons} \end{gathered}$

If the car has traveled for 246 miles, it will have 7.8 gallons left in the tank.

• Part d.

To write the equation, we have:

$x=16-\frac{d}{30}$