Algebra confusion

Spiltbeans

New member
Joined
Feb 7, 2019
Messages
1
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
Joined
Apr 22, 2015
Messages
1,380
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:
 
Top