Bob beats Judy by-10 m in a l00m dash. Bob, claiming to give Judy an equal chance, agrees to race her again but to start from 10 m behind the starting line. Does this really give Judy an equal chance?

Now we consider the situation when Bob decides to start 10 meters behind the starting line. Therefore the distance traveled by the Bob now is x+10 meters.
Assuming that the Bob maintains his average speed as v_b, we can calculate the time (say t’)taken by the Bob to reach the finish line as:


Substituting the value of v_b from equation (1) and the given value of x , we have

Judy, on the other hand has to travel distance x with the same average speed, and therefore the time (say t”) after which he will reach the finish line can be calculated as:


Substituting the value of v_j from equation (2) and the given value of x, we have


Thus we find that t’‘ > t’.
Therefore with same average speed and under the condition that the Bob started from
10 meters behind the starting line, Bob will still manage to reach the finish line earlier than Judy.

 

 

 

Regards

Arun (askIITians forum expert)