In 1 km races, runner 1 on track 1 (with time 2 min, 28.13 s) appears to be faster than runner 2 on track 2 (2 min, 28.48 s). however, the length l2 of track 2 might be slightly greater than the length l1 of track 1. how large can l2 − l1 be for us still to conclude that runner 1 is faster?

We are given with a velocity-distance-time kinematic problem given the different times of two runners and is asked for the difference in distances the runner has ran in the track. we use the formula v= d/t where d is the distance of running, t is time and v is the velocity of the runner. 

First runner, 
v = d/t = 1000 m / (120+28.13s ) = 6.750826976 m/s
Second runner
Using the same velocity we determine d2.
v = d2/t2 = d2 / (120+28.48s) = 6.750826976 m/s ; d2 = 1002.362789

distance of running track is the difference of the two distance achieved by the runners, delta d= d2 - d = 2.362789 m 

Nucleus for question ome

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