Question

When Darcy's car odometer reading is 43,440 miles, she fills her tank from LaTeX: \frac{1}{4} to full using 11 gallons of gasoline. When her gas gauge returns back to LaTeX: \frac{1}{4} full, her odometer reading is 43,649.



What is her gas mileage in miles per gallon?

21 MPG
22 MPG
20 MPG
19 MPG

Answer 1

To find Darcy's gas mileage in miles per gallon, we need to calculate the total miles driven while the gas gauge went from \(\frac{1}{4}\) full to \(\frac{1}{4}\) full again, and then divide that by the number of gallons used.

1. **Calculate the distance driven:**
- The starting odometer reading is 43,440 miles.
- The odometer reading when the gas gauge returns to \(\frac{1}{4}\) full is 43,649 miles.
- The distance driven is:
\[
43,649 - 43,440 = 209 \text{ miles}
\]

2. **Calculate the gallons used:**
- Darcy filled her tank from \(\frac{1}{4}\) to full using 11 gallons of gasoline. Therefore, when the gas gauge returned to \(\frac{1}{4}\) full, she used 11 gallons of gasoline.

3. **Calculate the gas mileage:**
- Gas mileage in miles per gallon (MPG) is calculated as:
\[
\text{MPG} = \frac{\text{miles driven}}{\text{gallons used}} = \frac{209 \text{ miles}}{11 \text{ gallons}}
\]
- Performing the division:
\[
\text{MPG} = \frac{209}{11} \approx 19
\]

Thus, Darcy's gas mileage is approximately **19 MPG**.