At t = 0, there is no road obviously. After the stretch, it starts at 1000.
At t = 1, there is 1m of road before him, 999 in front of him and after stretch 2 before him and 1998 in front of him.
At t = 3, 3m before him, 1997 in front, after stretch 4.5 before 2995.5 in front.
t = 4 5.5 before, 2994.5 in front; after stretch, 22/3 behind, 3992 and 2/3 in front...
ETC. Each time I am multiplying the ratio by 2/1 and then 3/2 and then 4/3 .... etc. The denominator and numerator increased by 1 each time.
Now obviously I need to try make a series out of this and determine if it converges of diverges to see if he will ever catch him. And then I need to come up with a general way formula for the questions for: "Can I save him sometimes,
but not others? If and when I can save him, how long will it take in each case?" Etc.
Now if you let d(1) [note (n) in front of d is just a subscript)] = x
d(2) = (x+1)((n+1)/n)
d(3) = ((x+1)((n+1))/n)+1)((n+1)/(n))
d(4) = .......(same thing with + 1 and then multiplying by ((n+1)/(n)).
A series is starting to develop. I'm a little stuck trying to create a geometric or harmonic series from this. Any thoughts?