John and David had a 100-meter race.
In the first race, John finished the race when David was at the 99-meter mark. However, David wanted another race. So John said, "This time, I will start 1 meter behind the starting line. That means I run 101 meters while you run 100 meters. And we both start together,". David agreed and there was another race.
If their speed in the second race were the same with that in the first race, who would reach the finish line first?
Let 'x' be the time john runs 100 'x' is also the time david runs 99
rate = 100/x rate = 99/x
for 101 meters for 100 m
time = 101m/ (100/x) = 101/100 = 1.01 x time = 100 m / (99/x) = 100/99 x = 1.010101x
So John will STILL win the race ! (by a hair !) because david's time is greater......
If you think about it, this makes sense.... John runs a meter faster than David does....that is why he wins the 100 meter in the first place.
adding ONE meter to each of their distances will result in John running THAT meter faster than David too....and John wins again !