The Gasoline Octane Problem

Authors

W.S. (Travis) Thompson, Harding University

Document Type

Article

Publication Title

MathAMATYC Educator

Publication Date

Spring 2024

Volume

15

Issue

3

First Page

10

Last Page

11

Abstract

The article discusses the gasoline octane problem and explores the assumption that mixing equal amounts of 89 octane and 93 octane gasoline will result in a full tank of 91 octane, which is the rating Mr. Smith's car requires. However, the article proves that this assumption is incorrect and presents a recursive equation that captures the octane rating on successive fill-ups. The article also discusses the solution to the recurrence relation using the Principle of Mathematical Induction. The conclusion is that the recursive sequence has two accumulation points of 91 ± (2/3). The article suggests further investigations, such as exploring the impact of initially filling the tank with 93-octane gasoline and finding a refill marker for the octane game to converge to a single limit point. [Extracted from the article]

Copyright held by

MathAMATYC Educator

Recommended Citation

Thompson, W. (. (2024). The Gasoline Octane Problem. MathAMATYC Educator, 15 (3), 10-11. Retrieved from https://scholarworks.harding.edu/math-facpub/1