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Consortium for Mathematics and its Applications

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Resource Type: Contest Problem
Primary Level: High School

Preventing Road Rage

Author: COMAP


Background:

In some cases, the road simply loses a lane as it enters a less traveled section. In other cases, the road narrows because of construction or roadwork. When this happens on a fairly busy highway, it may be a recipe for road rage.

Assume we’re on a busy two-lane road reducing to a one-lane road. Once a driver sees a sign indicating the right lane is going to end, he or she has a choice: drive in the right lane or drive in the left lane. Often, many drivers move into the left lane fairly quickly. This causes the left lane to become congested and slow down. Some drivers remain in the right lane and are able to maintain their speed (and pass the vehicles in the left lane which are now moving slower).

When a lane closure is approaching, there will be signs indicating the distance of the lane closure as it nears (e.g. 1 mile, 1/2 mile, 500 ft.). As the end of the right lane approaches, some of the right lane drivers merge into the left lane, while others continue heading toward the lane closure. It’s at this point that the probability of road rage rapidly increases. Horns blast and gestures are made. Some cars will pull half way into the right lane in an attempt to prevent any cars from passing only to have another vehicle swerve around them and continue toward the lane closure point. At times, a vehicle will stay in the right lane directly next to, and driving at the same speed as, a chosen vehicle in the left lane in an effort to make the travel toward the lane closure "fair."

Problem Download

©2015 by COMAP, Inc.
HiMCM Problem
Commentary: Yes (1) | Student Papers: Yes (4)

Mathematics Topics:

Math Modeling

Application Areas:

Contest Preparation

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