Question
Mayerlin filled up her car with gas before embarking on a road trip across the country. The capacity of Mayerlin's gas tank is 15 gallons and the car uses 0.75 gallons of gas for every hour driven. Make a table of values and then write an equation for G, commaG, in terms of t, commat, representing the number of gallons of gas remaining in Mayerlin's gas tank after tt hours of driving.
Number of Hours Driven Number of Gallons Remaining in the Tank
0
1
2
3
Number of Hours Driven Number of Gallons Remaining in the Tank
0
1
2
3
Answers
GPT-4o mini
To create a table for the number of gallons remaining in Mayerlin's gas tank after driving for a certain number of hours, we will start with the total capacity of the gas tank and subtract the amount of gas used over time.
Mayerlin's gas tank capacity is 15 gallons and her car consumes 0.75 gallons of gas per hour.
Now, we can calculate the number of gallons remaining after driving for each hour:
- At \( t = 0 \) hours, the remaining gas is \( 15 - (0.75 \times 0) = 15 \) gallons.
- At \( t = 1 \) hour, the remaining gas is \( 15 - (0.75 \times 1) = 15 - 0.75 = 14.25 \) gallons.
- At \( t = 2 \) hours, the remaining gas is \( 15 - (0.75 \times 2) = 15 - 1.5 = 13.5 \) gallons.
- At \( t = 3 \) hours, the remaining gas is \( 15 - (0.75 \times 3) = 15 - 2.25 = 12.75 \) gallons.
Now we can summarize this data in a table:
| Number of Hours Driven (t) | Number of Gallons Remaining (G) |
|----------------------------|----------------------------------|
| 0 | 15 |
| 1 | 14.25 |
| 2 | 13.5 |
| 3 | 12.75 |
Next, we can write an equation for \( G \), the number of gallons of gas remaining in Mayerlin's gas tank as a function of \( t \), the number of hours driven.
### Equation:
The gas remaining can be expressed as:
\[
G(t) = 15 - 0.75t
\]
Where:
- \( G(t) \) is the number of gallons of gas remaining after \( t \) hours.
- \( 15 \) is the initial amount of gas in gallons.
- \( 0.75 \) is the rate at which the gas is consumed in gallons per hour.
- \( t \) is the number of hours driven.
Mayerlin's gas tank capacity is 15 gallons and her car consumes 0.75 gallons of gas per hour.
Now, we can calculate the number of gallons remaining after driving for each hour:
- At \( t = 0 \) hours, the remaining gas is \( 15 - (0.75 \times 0) = 15 \) gallons.
- At \( t = 1 \) hour, the remaining gas is \( 15 - (0.75 \times 1) = 15 - 0.75 = 14.25 \) gallons.
- At \( t = 2 \) hours, the remaining gas is \( 15 - (0.75 \times 2) = 15 - 1.5 = 13.5 \) gallons.
- At \( t = 3 \) hours, the remaining gas is \( 15 - (0.75 \times 3) = 15 - 2.25 = 12.75 \) gallons.
Now we can summarize this data in a table:
| Number of Hours Driven (t) | Number of Gallons Remaining (G) |
|----------------------------|----------------------------------|
| 0 | 15 |
| 1 | 14.25 |
| 2 | 13.5 |
| 3 | 12.75 |
Next, we can write an equation for \( G \), the number of gallons of gas remaining in Mayerlin's gas tank as a function of \( t \), the number of hours driven.
### Equation:
The gas remaining can be expressed as:
\[
G(t) = 15 - 0.75t
\]
Where:
- \( G(t) \) is the number of gallons of gas remaining after \( t \) hours.
- \( 15 \) is the initial amount of gas in gallons.
- \( 0.75 \) is the rate at which the gas is consumed in gallons per hour.
- \( t \) is the number of hours driven.