# Algebra word problem

### Algebra word problem

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?
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### Re: Algebra word problem

"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."
Check the units: g(d), on the left, is a number of gallons so the right side must also be in gallons. That means that "15" must be "15 gallons" and since "d" is miles, that "20" must be "20 miles per gallon". In particular since g(d)= 0 when d/20= 15 gallons, I think we can safely assume that the capacity of the tank is 15 gallons of gas. In that case, the car gets 20 miles per gallon in the city.

"He can cover 3 more miles per gallon of gas on a highway within the city."
(I think you mean "than within the city".)
So he gets 23 miles per gallon on the highway.

"What is the maximum distance the car can travel on the highway with the tank filled to its capacity?"
The gas tank holds 15 gallons and, on the highway he gets 23 miles per gallon. Can you complete this?
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