Question
The graph shows the relationship between distance driven and gallons of gas used.
Continuous graph on a coordinate plane shows distance driven, numbered 20 to 60 along the horizontal axis, and gallons of gas used, numbered 1 to 4 on the vertical axis. Solid circles appear at points (0, 0), (30, 1), (60, 2).
Use the graph to complete the statements.
The car gets
miles to the gallon.
After the car has traveled
miles, 2 and two-thirdsgallons of gas have been consumed.
Continuous graph on a coordinate plane shows distance driven, numbered 20 to 60 along the horizontal axis, and gallons of gas used, numbered 1 to 4 on the vertical axis. Solid circles appear at points (0, 0), (30, 1), (60, 2).
Use the graph to complete the statements.
The car gets
miles to the gallon.
After the car has traveled
miles, 2 and two-thirdsgallons of gas have been consumed.
Answers
GPT-4o mini
To determine how many miles the car gets per gallon, we can use the points provided on the graph.
From the points listed:
- At (30, 1): This means that after driving 30 miles, 1 gallon of gas has been used.
- At (60, 2): This means that after driving 60 miles, 2 gallons of gas have been used.
To find miles per gallon, we can calculate the average rate based on these points.
1. For the first point:
\[
\text{Miles per gallon} = \frac{\text{Distance driven}}{\text{Gallons used}} = \frac{30 \text{ miles}}{1 \text{ gallon}} = 30 \text{ miles per gallon}
\]
2. For the second point:
\[
\text{Miles per gallon} = \frac{60 \text{ miles}}{2 \text{ gallons}} = 30 \text{ miles per gallon}
\]
So, the car gets **30 miles to the gallon**.
Next, we need to find out how far the car has traveled when 2 and two-thirds gallons of gas have been consumed. Two and two-thirds gallons is the same as \(\frac{8}{3}\) gallons.
To find the distance driven corresponding to this amount of gas, we can use the relationship established in the previous calculations. Since the car gets 30 miles to the gallon, we can calculate the distance as follows:
\[
\text{Distance} = \text{Gallons used} \times \text{Miles per gallon} = \frac{8}{3} \times 30
\]
Calculating this gives us:
\[
\text{Distance} = \frac{8 \times 30}{3} = \frac{240}{3} = 80 \text{ miles}
\]
Thus, after the car has traveled **80 miles**, 2 and two-thirds gallons of gas have been consumed.
To summarize:
- The car gets **30 miles to the gallon**.
- After the car has traveled **80 miles**, 2 and two-thirds gallons of gas have been consumed.
From the points listed:
- At (30, 1): This means that after driving 30 miles, 1 gallon of gas has been used.
- At (60, 2): This means that after driving 60 miles, 2 gallons of gas have been used.
To find miles per gallon, we can calculate the average rate based on these points.
1. For the first point:
\[
\text{Miles per gallon} = \frac{\text{Distance driven}}{\text{Gallons used}} = \frac{30 \text{ miles}}{1 \text{ gallon}} = 30 \text{ miles per gallon}
\]
2. For the second point:
\[
\text{Miles per gallon} = \frac{60 \text{ miles}}{2 \text{ gallons}} = 30 \text{ miles per gallon}
\]
So, the car gets **30 miles to the gallon**.
Next, we need to find out how far the car has traveled when 2 and two-thirds gallons of gas have been consumed. Two and two-thirds gallons is the same as \(\frac{8}{3}\) gallons.
To find the distance driven corresponding to this amount of gas, we can use the relationship established in the previous calculations. Since the car gets 30 miles to the gallon, we can calculate the distance as follows:
\[
\text{Distance} = \text{Gallons used} \times \text{Miles per gallon} = \frac{8}{3} \times 30
\]
Calculating this gives us:
\[
\text{Distance} = \frac{8 \times 30}{3} = \frac{240}{3} = 80 \text{ miles}
\]
Thus, after the car has traveled **80 miles**, 2 and two-thirds gallons of gas have been consumed.
To summarize:
- The car gets **30 miles to the gallon**.
- After the car has traveled **80 miles**, 2 and two-thirds gallons of gas have been consumed.