# Algebra confusion

#### Spiltbeans

##### New member
After checking that the gas tank of a car is filled to its capacity, a person proves the following:
Travelling d miles within a city, the number of gallons of gas left in the tank can be given by the function g(d)=15-d/20.
He can cover 3 more miles per gallon of gas on a highway within the city.
What is the maximum distance the car can travel on the highway with the tank filled to its capacity?

#### Otis

##### Senior Member
g(d) = 15 - (1/20)(d)

Let's think about what this function does. We know that g(d) is the number of gallons left in the tank after driving d miles.

Well, if we don't drive at all, then the tank is still full. It's easy to see that g(0) is 15 gallons (a full tank).

Let's drive 1 mile.

g(1) = 15 - 1/20

In other words, function g subtracts 1/20th of a gallon, for each mile driven.

That's enough information to write a miles/gallon ratio, because it shows 1/20th gallon used for driving 1 mile.

$$\displaystyle \dfrac{1}{\frac{1}{20}} \dfrac{\text{mi}}{\text{gal}}$$

Simplify that compound fraction, and you'll know the miles-per-gallon for city driving.

Is that enough information, to get to the finish line? If not, please show how far you got. :cool: