Part A In Europe, gasoline efficiency is measured in \( \mathrm{km} / \mathrm{L} \). If your car's gas mileage is \( 26.0 \mathrm{mi} / \) gal, how many liters of gasoline would you need to buy to complete a 142 -km trip in Europe? Use the following conversions: \( 1 \mathrm{~km}=0.6214 \mathrm{mi} \) and \( 1 \mathrm{gal}=3.78 \mathrm{~L} \). Express your answer numerically in liters.

To find out how many liters of gasoline you would need for a 142-km trip, we first need to convert the distance from kilometers to miles, and then use the car's gas mileage to determine how many gallons are needed, and finally convert that to liters. 1. **Convert kilometers to miles:** \[ \text{Distance in miles} = 142 \, \text{km} \times \frac{0.6214 \, \text{mi}}{1 \, \text{km}} = 88.2358 \, \text{mi} \] 2. **Calculate the number of gallons needed:** Given that the car's gas mileage is \( 26.0 \, \text{mi/gal} \): \[ \text{Gallons needed} = \frac{\text{Distance in miles}}{\text{Gas mileage}} = \frac{88.2358 \, \text{mi}}{26.0 \, \text{mi/gal}} \approx 3.3967 \, \text{gal} \] 3. **Convert gallons to liters:** Using the conversion \( 1 \, \text{gal} = 3.78 \, \text{L} \): \[ \text{Liters needed} = 3.3967 \, \text{gal} \times 3.78 \, \text{L/gal} \approx 12.837 \, \text{L} \] Thus, the amount of gasoline needed for the trip is approximately \( \boxed{12.84} \) liters.