100 meters race riddle
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Akash, Andrew, and Allen race each other in a 100 meters race. All of them run at a constant speed throughout the race.
Akash beats Andrew by 20 meters.
Andrew beats Allen by 20 meters.
How many meters does Akash beat Allen by?
Akash takes the race first in unity time. Therefore
100 = v_akash * 1
At this unity time, Andrew lags by 20 meters. Therefore
80 = v_andrew *1
Andrew finishes the race in time t_2. Therefore using the last relation
100 = 80 t_2
or t_2 = 10/8
At this time t_2, we know that andrew beats allen by twenty meters. So Allen is at 80 meters at time t_2
80 = v_allen * 10/8
or v_allen = 64.
So at t_1, Allen is at 64m. So Akash beats Allen by 100 – 64 = 36 m.
36 meters
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