Match each vehicle scenario to its calculated maximum usable travel range in miles.

Delivery Truck: Has a $40$ -gallon tank. It uses $60\%$ of its fuel in city traffic at $12$ mpg, and the remaining $40\%$ on highways at $20$ mpg. $608$ miles
Patrol Boat: Holds $120$ gallons of fuel but is required to maintain a $20\%$ reserve. Operates at a constant efficiency of $6$ mpg. $576$ miles
Light Aircraft: Holds $300$ gallons of fuel. It burns $30$ gallons during an initial $50$ -mile ascent, then maintains a cruise efficiency of $2$ mpg with the remaining fuel. $590$ miles
Recreational Vehicle: Burned $40$ gallons during a previous $480$ -mile trip. Assuming the exact same efficiency, it now operates on a full $52$ -gallon tank. $624$ miles

Answer

The correct matches are: Delivery Truck corresponds to 608 miles, Patrol Boat corresponds to 576 miles, Light Aircraft corresponds to 590 miles, and Recreational Vehicle corresponds to 624 miles.

Each vehicle's range is properly determined by finding the product of its available fuel and fuel efficiency rate for each specific segment of travel, ensuring reserves and phase-specific rates are accurately applied.

Step-by-Step Solution

Calculate the maximum range for the Delivery Truck.

City range is

288

miles and highway range is

320

miles, yielding a total of

608

miles.

Efficiency varies by driving condition, so total range is the sum of the calculated ranges for each proportional fuel segment.

Calculate the maximum range for the Patrol Boat.

Usable fuel is

96

gallons, yielding a range of

576

miles.

The

20\%

mandatory reserve cannot be used for the travel range calculation, meaning only

80\%

of the tank is available.

Calculate the maximum range for the Light Aircraft.

Remaining fuel is

270

gallons providing a cruise range of

540

miles. Adding the initial

50

miles yields

590

miles.

Total range includes both the ascent distance and the subsequent cruise distance.

Calculate the maximum range for the Recreational Vehicle.

Efficiency is

12

mpg, leading to a maximum range of

624

miles on a

52

-gallon tank.

The efficiency rate is constant, so it is derived from the prior trip and applied to the new full tank.

Key Concept

Calculating maximum range by determining usable fuel volumes and applying multiple rates of efficiency.

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