Final answer:
By setting up two equations with the given data and using the elimination method, we find that the fuel efficiency of the car on the highway is 28 miles per gallon.
Step-by-step explanation:
In order to find out the fuel efficiency of the car on highway driving, we will use the details of the two trips made by the car. There are two unknowns in this problem: the fuel efficiency in the city (C) and the fuel efficiency on the highway (H). We will set up two equations based on the given data and then solve for H.
From the first trip, we have the equation:
120/C + 280/H = 16 (since both city and highway driving used up one tank of 16 gallons).
From the second trip, we have the equation:
220/C + 140/H = 16 (since the second tankful was also 16 gallons).
We can solve these two equations as a system to find C and H. However, we are only interested in the highway fuel efficiency (H), so we will use the elimination method to solve for H.
Multiply both sides of the first equation by 220 and both sides of the second equation by 120 and subtract them to find H.
The calculation would look like this:
- 26400/C + 61600/H = 3520
- 26400/C + 16800/H = 1920
- Subtracting the second equation from the first gives:
- 44800/H = 1600
- H = 44800/1600
- H = 28 miles per gallon
Therefore, the fuel efficiency of this car on the highway is 28 miles per gallon.