Question
Tracy is.
On a cross-country road trip, she stops at a restaurant station to feel her gas tank and plans to drive for another 6 hours along the highway. Before making her next stop. There is a liner relationship between the time in hours since Tracy filled the car with gas and the amount of gas left the tank in gallons. Describe the rate of change for this relationship
The amount of gas left by blank per hour
Does it increases or decreases
2 7.
Ths of a gallon
Two fifths of a gallon
Two gallons
Two and a half gallons
Three and a half gallons
Five gallons
On a cross-country road trip, she stops at a restaurant station to feel her gas tank and plans to drive for another 6 hours along the highway. Before making her next stop. There is a liner relationship between the time in hours since Tracy filled the car with gas and the amount of gas left the tank in gallons. Describe the rate of change for this relationship
The amount of gas left by blank per hour
Does it increases or decreases
2 7.
Ths of a gallon
Two fifths of a gallon
Two gallons
Two and a half gallons
Three and a half gallons
Five gallons
Answers
GPT-4o mini
To determine the rate of change of the amount of gas left in Tracy's tank, we first need to clarify what the relationship implies. If there is a linear relationship between time (in hours) and the amount of gas left in the tank (in gallons), we can describe this relationship in terms of the rate of gas consumption over time.
Let's analyze the options provided for the gas consumption rate:
1. **Two fifths of a gallon per hour**
2. **Two gallons per hour**
3. **Two and a half gallons per hour**
4. **Three and a half gallons per hour**
5. **Five gallons per hour**
Since the problem suggests that the amount of gas left in the tank decreases over time, the rate of change will be negative. This means that if we use, for example, "two fifths of a gallon per hour," it would imply that for every hour Tracy drives, she consumes \( \frac{2}{5} \) of a gallon of gas.
### Summary of the Rate of Change:
- The rate of change is a negative value representing gas consumption.
- Therefore, if we interpret the options correctly, we would be looking at how many gallons she is using per hour.
#### Choosing a Rate
If we had to choose one of the options, let's assume:
- If Tracy is driving for 6 hours, and the amount of gas she started with was, for instance, 15 gallons, she would have to consume gas at a rate such that she still has some gas left after 6 hours.
Assuming the amount of gas Tracy uses helps her run out of gas after 6 hours, you would want to select a smaller consumption rate from the given options to ensure she has enough gas left.
So if she consumes:
- **Two fifths of a gallon per hour**, over 6 hours that would be \( 6 \times \frac{2}{5} = \frac{12}{5} \) gallons or 2.4 gallons used in total.
Thus, if she started with 10 gallons, she would have 7.6 gallons left, which would indicate a slower rate of consumption and may be reasonable.
### Final Answer:
- **Rate of Change**: Decreases
- **Amount of gas left**: **Two fifths of a gallon per hour**
This means her tank drops by \( \frac{2}{5} \) of a gallon for every hour she drives.
Let's analyze the options provided for the gas consumption rate:
1. **Two fifths of a gallon per hour**
2. **Two gallons per hour**
3. **Two and a half gallons per hour**
4. **Three and a half gallons per hour**
5. **Five gallons per hour**
Since the problem suggests that the amount of gas left in the tank decreases over time, the rate of change will be negative. This means that if we use, for example, "two fifths of a gallon per hour," it would imply that for every hour Tracy drives, she consumes \( \frac{2}{5} \) of a gallon of gas.
### Summary of the Rate of Change:
- The rate of change is a negative value representing gas consumption.
- Therefore, if we interpret the options correctly, we would be looking at how many gallons she is using per hour.
#### Choosing a Rate
If we had to choose one of the options, let's assume:
- If Tracy is driving for 6 hours, and the amount of gas she started with was, for instance, 15 gallons, she would have to consume gas at a rate such that she still has some gas left after 6 hours.
Assuming the amount of gas Tracy uses helps her run out of gas after 6 hours, you would want to select a smaller consumption rate from the given options to ensure she has enough gas left.
So if she consumes:
- **Two fifths of a gallon per hour**, over 6 hours that would be \( 6 \times \frac{2}{5} = \frac{12}{5} \) gallons or 2.4 gallons used in total.
Thus, if she started with 10 gallons, she would have 7.6 gallons left, which would indicate a slower rate of consumption and may be reasonable.
### Final Answer:
- **Rate of Change**: Decreases
- **Amount of gas left**: **Two fifths of a gallon per hour**
This means her tank drops by \( \frac{2}{5} \) of a gallon for every hour she drives.