Solve Homework: Determine Max L2-L1 for Runner 1 to be Faster

AI Thread Summary
To determine the maximum difference in lengths L2 and L1 for runner 1 to still be considered faster, the equation L2t1 - L1t2 < 0 is used. By substituting L1 with 1 km, the focus shifts to finding the maximum permissible value for L2 - L1. The discussion emphasizes the importance of the relationship between time and distance in calculating speed. Participants are encouraged to explore the implications of track length differences on speed conclusions. Ultimately, the goal is to establish a clear threshold for the length discrepancy that allows for a valid comparison of the runners' speeds.
GunnaSix
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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.
 
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Hi GunnaSix! :smile:

Why not just put L1 = 1 km?
 
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