Question

In 1 km races, runner 1 on track 1(with time 2 min,27.95 s) appears to be faster than runner 2 on track 2 ( 2 min, 28.15 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 still to conclude that runner 1 is faster?

Answer 1

L₂ - L₁ can be a maximum 1.5 meters for us to still conclude that runner 1 is faster

Explanation :

For runner 1,

Distance, L₁ = 1 km = 1000 m

Time = 2 min 27.95 sec = 147.95

=> speed of runner 1 = distance/time

=> s = 1000/147.95 = 6.76 m/s

For runner 1 to be faster than runner 2, the speed of runner 2 should be less than 6.76 m/s

Distance = L₂

Time = 2 min 28.15 sec = 148.15 sec

=> L₂/148.15 < 6.76

=> L₂ < 6.76 x 148.15

=> L₂ < 1001.5 m

Hence L₂ - L₁ = 1001.5 - 1000 = 1.5 m

Thus L₂ - L₁ can be a maximum 1.5 meters for us to still conclude that runner 1 is faster