I hope I'll be able to answer this question well.
when dilling with paradox you need to remember that the paradox it written so to confuse you. and make you think about the problem describe in a way to confuse you.
first of all, you know for a fact that the rabbit will be the first to cross the end-line if it is far enough. the only question is how far is far enough.
what happen if the rabbit go 10 times as fast as the turtle and the turtle gets 10 meter head start? at the at the time the rabbit gets to the starting point of the turtle will get far by one meter. so the rabbit get another meter the turtle move 10 more cm etc.
what happen if the race is for 20 meters? the rabit go for the first 10 meter and the rabit is 9 meter away from the end line. at the next 10 meter the rabit is crossing the line while the turtle is 8 meter from the crossing line.
the situation is the same for 19, 18, 17... meter the question is at what distance will they cross the line at the same time? we can calculate it using it with the following expression:
infinite series
our series is the distance of the turtle has passed from the earlier period of time
1 , 0.1 , 0.01, ...
and q is the ratio between to cases, 0.1
so the sum is 1/0.9 = 1.11111.... at that distance (from the starting point of the turtle) the rabbit and the turtle will cross the line at the same time.
I believe my explanation isn't that well but I hope it helped you tho.