Max difference L2 - L1 for runner 1 to be faster

[GunnaSix]

Homework Statement

In 1 km races, runner 1 on track 1 (with time t₁ = 147.95 s) appears to be faster than runner 2 on track 2 (t₂ = 148.15 s). However, length L₂ of track 2 might be slightly greater than length L₁ of track 1. How large can L₂ - L₁ be for us to still conclude that runner 1 is faster?

Homework Equations

v = L / t

The Attempt at a Solution

I got it down to L₂t₁ - L₁t₂ < 0, but can't figure out how to get L₂ - L₁ out. I know I probably have to use the fact that L is approximately 1 km, but I'm not seeing how to do it.

 

[tiny-tim]

Hi GunnaSix!

Why not just put L₁ = 1 km?