Sequence prob: boys running on ever-lengthening roadway

[chillerbros17]

There are 2 boys standing on a road, one kilometer apart from eachother. The boys names are Pete and John. Pete starts to run after John, moving at 1 meter per second. After 1 second the road stretches uniformly and instantaneously by 1 kilometer so now John is 1998 meters away from Pete. Pete tries to speed up but is still moving at 1 meter per second. After another second the road stretches again by 1 kilometer so now Pete is 2995.5 meters away. This keeps happening over and over again.

Does Pete ever catch up to John?

If he does, how long does it take?

Set up a sequence where Dn represents the distance between Pete and John after n seconds, but before the road does its instantaneous stretch(immediately after the step but before the stretch)

Find a general expression for Dn in terms of D0

 

[TchrWill]

There are 2 boys standing on a road, one kilometer apart from eachother. The boys names are Pete and John. Pete starts to run after John, moving at 1 meter per second. After 1 second the road stretches uniformly and instantaneously by 1 kilometer so now John is 1998 meters away from Pete. Pete tries to speed up but is still moving at 1 meter per second. After another second the road stretches again by 1 kilometer so now Pete is 2995.5 meters away. This keeps happening over and over again.

Does Pete ever catch up to John?

If he does, how long does it take?

Set up a sequence where Dn represents the distance between Pete and John after n seconds, but before the road does its instantaneous stretch(immediately after the step but before the stretch)

Unless I missed something, with Pete moving only 1 meter every second, there is no way that he can ever catch John. n = the end of the second before the road stretch. Dn is the distance between Pete snd John at that instant in time before the road stretch. Dp is the distace Pete has moved each second.

n........1.......2.......3.......4.......5........6.......6.......7.......8........9.......10
Dn....999..1998..2997..3996..4995..5994..6993..7992..8991..9990..10989
Dp.....1.......2.......3........4.......5.......6.......7.......8.......9.......10.......11