Two friends, Deondra and Nabhitha, had just bought their first cars. The equation y, equals, 42, point, 2, xy=42.2x represents the number of miles, yy, that Deondra can drive her car for every xx gallons of gas. The table below represents the number of miles, yy, that Nabhitha can drive her car for every xx gallons of gas.

Nabhitha's Gas Mileage
Gallons left parenthesis x right parenthesisGallons (x) Miles left parenthesis y right parenthesisMiles (y)
22 8080
55 200200
1212 480480
1414 560560
How much farther can Deondra's car travel on one gallon of gas than Nabhitha's car?

1 answer

To determine how much farther Deondra's car can travel on one gallon of gas compared to Nabhitha's car, we first need to find the distance Deondra can travel for one gallon of gas based on the equation given:

\[ y = 42.2x \]

When \( x = 1 \) (for one gallon of gas), we can find y as follows:

\[ y = 42.2(1) = 42.2 \]

So, Deondra can travel 42.2 miles on one gallon of gas.

Next, we will look at Nabhitha's gas mileage from the provided table to find out how far she can travel on one gallon of gas. Here are the entries converted into miles per gallon:

  • For \( x = 2 \) gallons: \[ \text{Miles per gallon} = \frac{80}{2} = 40 \text{ miles/gallon} \]

  • For \( x = 5 \) gallons: \[ \text{Miles per gallon} = \frac{200}{5} = 40 \text{ miles/gallon} \]

  • For \( x = 12 \) gallons: \[ \text{Miles per gallon} = \frac{480}{12} = 40 \text{ miles/gallon} \]

  • For \( x = 14 \) gallons: \[ \text{Miles per gallon} = \frac{560}{14} = 40 \text{ miles/gallon} \]

From these calculations, we can see that Nabhitha's car also has a gas mileage of 40 miles per gallon.

Now, we can determine how much farther Deondra's car can travel on one gallon of gas compared to Nabhitha's car:

\[ \text{Distance Difference} = \text{Distance Deondra can travel} - \text{Distance Nabhitha can travel} \] \[ \text{Distance Difference} = 42.2 - 40 = 2.2 \text{ miles} \]

Therefore, Deondra's car can travel 2.2 miles farther on one gallon of gas than Nabhitha's car.