Question

If a certain automobile gets between 20 and 24 miles per gallon of gasoline, inclusive, what would be the maximum amount of gasoline, in gallons, this automobile would consume on a trip of 360 miles?

• A. 20.0
• B. 18.0
• C. 16.4
• D. 16.0
• E. 15.0

Hint:

Be careful with keywords like "maximum" and "minimum". In problems involving rates like this, maximizing one quantity (consumption) often requires minimizing a related quantity (efficiency).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The amount of gasoline consumed is inversely proportional to the car's fuel efficiency (miles per gallon). To find the maximum amount of gasoline consumed, we must use the minimum fuel efficiency.
Step 2: Key Formula or Approach:
The formula to calculate gasoline consumption is:
\[ \text{Gasoline Consumed} = \frac{\text{Total Distance}}{\text{Miles Per Gallon}} \] To maximize the "Gasoline Consumed", we need to minimize the denominator, "Miles Per Gallon".
Step 3: Detailed Explanation:
The total distance of the trip is 360 miles.
The fuel efficiency range is between 20 and 24 miles per gallon (mpg), inclusive.
The minimum fuel efficiency is 20 mpg.
Now, we calculate the maximum gasoline consumption using the minimum fuel efficiency:
\[ \text{Maximum Gasoline Consumed} = \frac{360 \text{ miles}}{20 \text{ mpg}} \] \[ \text{Maximum Gasoline Consumed} = \frac{36}{2} \text{ gallons} = 18 \text{ gallons} \] Step 4: Final Answer:
The maximum amount of gasoline the automobile would consume is 18.0 gallons.