Problem Solving

A car traveled 462 miles per tankful of gasoline on the highway and 336 miles per tankful of gasoline in the city. If the car traveled 6 fewer miles per gallon in the city than on the highway, how many miles per gallon did the car travel in the city?

(A) 14
(B) 16
(C) 21
(D) 22
(E) 27

The OA is B.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I need your help. Thanks.

Hi swerve,
Let's take a look at your question.

On Highway, using a tank full of gasoline a car traveled = 462 miles
In city, using a tank full of gasoline a car traveled = 336 miles

Let, On Highway, miles per gallon the car traveled = x miles, then
In city, miles per gallon the car traveled = (x-6) miles

We will be using ratios to solve this problem,
$$\frac{462}{336}=\frac{x}{x-6}$$
$$\frac{231}{168}=\frac{x}{x-6}$$
$$231\left(x-6\right)=168x$$
$$231x-1386=168x$$
$$231x-168x=1386$$
$$63x=1386$$
$$x=\frac{1386}{63}$$
$$x=22$$

We need to find, how many miles per gallon did the car travel in the city?
In city, miles per gallon the car traveled = (x-6) miles
In city, miles per gallon the car traveled = 22-6 = 16 miles

Option B is correct.

Hope it helps.
I am available if you'd like any follow up.

A car traveled 462 miles per tankful of gasoline on the highway and 336 miles per tankful of gasoline in the city. If the car traveled 6 fewer miles per gallon in the city than on the highway, how many miles per gallon did the car travel in the city?

(A) 14
(B) 16
(C) 21
(D) 22
(E) 27

An alternate approach is to PLUG IN THE ANSWERS, which represent the miles per gallon in the city.
When the correct answer choice is plugged in, the same amount of gas -- in other words, ONE TANKFUL -- will be required to travel 336 miles in the city and 462 miles on the highway.

Since all of the values in the problem are INTEGERS, the correct answer choice must divide evenly into the distance traveled in the city (336).
336 = 2*3*7*8.
Eliminate D (2*11) and E (3*3*3), neither of which divides evenly into 2*3*7*8.

Since on the highway 6 more miles per gallon are traveled, 6 more than the correct answer choice must divide evenly into the distance traveled on the highway (462).
Adding 6 to each of the remaining answer choices, we get:
A: 14+6 = 20 = 2*2*5.
B: 16+6 = 22 = 2*11.
C: 21+6 = 27 = 3*3*3.
Since 462 = 2*3*7*11, only B (2*11) divides evenly into the distance traveled on the highway.

The correct answer is B.

Answer choice B: 16 miles per gallon in the city, 22 miles per gallon on the highway
At a rate of 16 miles per gallon, the amount of gas required to travel 336 miles in the city = 336/16 = 21 gallons.
At a rate of 22 miles per gallon, the amount of gas required to travel 462 miles on the highway = 462/22 = 21 gallons.
Success!
The same amount of gas -- 21 gallons -- is sufficient to travel 336 miles in the city and 462 miles on the highway.