Question

The following graph shows the mileage of Alex's car as he traveled from New York to Ohio. On the way back, the mileage of his car was $33.4$ miles per gallon. How much fuel did Alex use on his return journey? Did he use more fuel than he used during the first leg of his journey?
(($x$-axis: fuel consumed (in gallons), ($y$-axis: distance (in miles))

• A. Fuel consumed $=15.69$ gal, yes
• B. Fuel consumed $=13.24$ gal, yes
• C. Fuel consumed $=12.43$ gal, yes
• D. Fuel consumed $=10$ gal, yes

Answer 1

The correct option is A Fuel consumed $=15.69$ gal, yes

Let’s find the unit rate for fuel consumption using the given graph.



Unit rate for fuel consumption (mileage) $=\frac{523.97-0}{7.85-0}=\frac{523.97}{7.85}\approx 66.75\text{mi per gal}$

Therefore, the equation of the straight line is $y=66.75x.$
On the return journey, Alex’s mileage dropped to $33.4mipergal.$
So, the new equation will be $y=33.4x.$

We know the distance between the two cities from the graph.
$y=523.97mi$

Therefore, the fuel consumed on the return journey, $x=\frac{523.97}{33.4}=15.69gal$