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The gas mileage for a car is 2323 miles per gallon when the car travels at 6060 miles per hour. The car begins a trip with 1313 gallons in its tank, travels at an average speed of 6060 miles per hour for hh hours, and ends the trip with 1010 gallons in its tank. Which of the following equations best models this situation?\newlineChoose 11 answer:\newline(A) 13−23h60=1013-\frac{23h}{60}=10\newline(B) 13−60h23=1013-\frac{60h}{23}=10\newline(C) 13−60h23=10\frac{13-60h}{23}=10\newline(D) 13−23h60=10\frac{13-23h}{60}=10

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Q. The gas mileage for a car is 2323 miles per gallon when the car travels at 6060 miles per hour. The car begins a trip with 1313 gallons in its tank, travels at an average speed of 6060 miles per hour for hh hours, and ends the trip with 1010 gallons in its tank. Which of the following equations best models this situation?\newlineChoose 11 answer:\newline(A) 13−23h60=1013-\frac{23h}{60}=10\newline(B) 13−60h23=1013-\frac{60h}{23}=10\newline(C) 13−60h23=10\frac{13-60h}{23}=10\newline(D) 13−23h60=10\frac{13-23h}{60}=10
  1. Determine Gas Usage: We need to determine how much gas the car uses over hh hours when traveling at 6060 miles per hour. The car's gas mileage is 2323 miles per gallon, which means for every hour the car travels at 6060 miles per hour, it uses 6023\frac{60}{23} gallons of gas. Since the car starts with 1313 gallons and ends with 1010 gallons, the amount of gas used is 13−10=313 - 10 = 3 gallons. We need to find the equation that represents the relationship between the hours traveled (hh) and the gallons used.
  2. Calculate Gallons Used: To calculate the total gallons used over hh hours, we multiply the number of hours (hh) by the rate of gas consumption per hour (6023\frac{60}{23}). This gives us the equation (6023)h(\frac{60}{23})h for the gallons used.
  3. Equation Representation: Since the car starts with 1313 gallons and ends with 1010 gallons, the total gallons used should be subtracted from the initial amount of gas to equal the final amount of gas. Therefore, the equation should be 13−(6023)h=1013 - (\frac{60}{23})h = 10.
  4. Verify Answer Choice: Looking at the answer choices, we can see that option (B) 13−60h23=1013 - \frac{60h}{23} = 10 matches our derived equation. Therefore, the correct answer is (B).

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