Problem:
Roy bought a new battery-gasoline hybrid car. On a trip the car ran exclusively on its battery for the first miles, then ran exclusively on gasoline for the rest of the trip, using gasoline at a rate of gallons per mile. On the whole trip he averaged miles per gallon. How long was the trip in miles?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Let be the number of miles driven exclusively on gasoline. Then the total number of miles traveled is , and the amount of gas used is gallons. Therefore the average number of miles per gallon is
Solving results in , so the total number of miles traveled is .
The problems on this page are the property of the MAA's American Mathematics Competitions