To determine how many gallons of gasoline the car has left after it has traveled 330 miles, let’s analyze the given data and find the gas consumption rate as well as the remaining gas step by step:
First, we have the following distances and corresponding amounts of gas left in the tank:
| Distance Traveled (miles) | 0 | 90 | 180 | 270 |
|---------------------------|----|----|-----|-----|
| Gas Left in Tank (gallons)| 15 | 12 | 9 | 6 |
1. Calculate the rate of gas consumption per mile:
The total distance covered is from 0 miles to 270 miles.
[tex]\[
\text{Total Distance} = 270 - 0 = 270 \, \text{miles}
\][/tex]
The total amount of gas used in this distance is from 15 gallons to 6 gallons.
[tex]\[
\text{Total Gas Used} = 15 - 6 = 9 \, \text{gallons}
\][/tex]
The rate of gas consumption per mile can be calculated as:
[tex]\[
\text{Gas Consumption Rate} = \frac{\text{Total Gas Used}}{\text{Total Distance}} = \frac{9 \, \text{gallons}}{270 \, \text{miles}} = 0.0333 \, \text{gallons per mile}
\][/tex]
2. Calculate the amount of gas left after 330 miles:
To find out how much gas is left after traveling 330 miles, we use the calculated gas consumption rate.
The initial amount of gas is 15 gallons.
The total gas consumed over 330 miles is:
[tex]\[
\text{Gas Consumed} = \text{Gas Consumption Rate} \times \text{Distance Traveled} = 0.0333 \, \text{gallons per mile} \times 330 \, \text{miles} = 11 \, \text{gallons}
\][/tex]
Therefore, the amount of gas remaining in the tank after traveling 330 miles is:
[tex]\[
\text{Gas Remaining} = \text{Initial Gas} - \text{Gas Consumed} = 15 \, \text{gallons} - 11 \, \text{gallons} = 4 \, \text{gallons}
\][/tex]
Thus, after the car has traveled 330 miles, it will have 4 gallons of gasoline left in the tank.
