So we're looking for:

$\frac{miles}{gallon}$

and we're given:

$\frac{miles}{tank}$, where the tank consists of a fixed maximum number of gallons.


To find out the number of gallons in the tank, we can think of it as a ratio:

$\frac{gallons}{tank}$


Writing this out, we get:

$\frac{462 miles}{tank}$ on the highway.

$\frac{336 miles}{tank}$ in the city.

We also know that the car in the city drove 6 miles less than the car did on the highway. Let $x$ be the number of miles driven on the highway. It follows that $x-6$ miles we're driven in the city. This can be written as:

$\frac{(x)miles}{gallons}$ on the highway.

$\frac{(x-6)miles}{gallons}$ in the city.


To find the gallons per tank we can simply divide miles/tank by miles/gallons to eliminate the miles:

$\frac{462 miles}{tank} / \frac{(x) miles}{gallons}$

$\frac{336 miles}{tank} / \frac{(x-6) miles}{gallons}$

This simplifies to:

$(\frac{462 miles}{tank}) * (\frac{gallons}{(x) miles})$

$\frac{462 miles}{(x) miles}$ $\frac{gallons}{tank}$


And:

$\frac{336 miles}{tank} * \frac{gallons}{(x-6) miles}$

$\frac{336 miles}{(x-6) miles}$ $\frac{gallons}{tank}$

The miles cancel and we're left with:

$\frac{462}{x}$ $\frac{gallons}{tank}$

$\frac{336}{(x-6)}$ $\frac{gallons}{tank}$

Now we can simply equal them to eachother to solve for $x$:

$\frac{462}{x}$ $=$ $\frac{336}{(x-6)}$

$462x - 2772 = 336x$

$-2772 = -126x$

$x = 22$

Since we're looking for the number of miles per gallon incurred in the city, we would plug this into the miles per gallon equation written above for the city:

$\frac{(x-6)miles}{gallon}$ in the city.

$\frac{(22-6)miles}{gallon}$ in the city.

$\frac{16miles}{gallon}$ in the city.

So the answer is B