The Linear Race: A Linear Algebra Playground

Controls Panel

Runner 1 (The Leader)

m/s

Set the constant speed of Runner 1. This value represents the slope of Runner 1's line on the graph.

Runner 2 (The Chaser)

seconds

Set how many seconds Runner 1 gets to run before Runner 2 starts. This shifts Runner 2's starting point forward in time.

m/s

Set the constant speed of Runner 2. Notice how when this speed is greater than Runner 1's, a chase is possible. What happens if it's the same or less?

Visualization & Explanation

The Problem

System of Equations

This is a 'system of linear equations'. We are looking for the single point (time, distance) where both equations are true. This is the point where the lines cross on the graph.

Runner 1:

Runner 2:

The Solution