BTGModeratorVI wrote: ↑

Tue Dec 15, 2020 6:52 am

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

Answer: B
Source: official guide

The car burns a tankful of gas on the highway and a tankful of gas in the city.

So, we can start with this WORD EQUATION: (volume of gas used on the highway) = (volume of gas used in the city)

Key formula: gallons of gas used = (distance traveled)/(rate of miles traveled per gallon)
So, the word equation becomes: (distance traveled on highway)/(highway fuel consumption rate) = (distance traveled in city)/(city fuel consumption rate))

Let x = the rate of fuel consumption in the city (in miles per gallon)
So x+6 = the rate of fuel consumption on highway (in miles per gallon)
The car traveled 462 miles on the highway and 336 miles in the city.

Plug the values into the equation to get to get: 462/x+6 = 336/x
Cross multiply to get: 462x = 336(x + 6)
Expand to get: 462x = 336x + 2016
Subtract 336x from both sides to get: 126x = 2016
Solve: x = 2016/126 = 16

Answer: B

Cheers,
Brent