Well I managed to crank 11 equations out of this problem. There are 11 variables to consider so it should just be a matter of rearranging now. But I'm too exhausted to do it at this point so I'll just post what I found for now.

We'll let A = 0, and t = 0 be the time when they first begin. Also I changed jack and jill to boy and girl, so we can represent them with different letters.

1. The position (or distance traveled from A) when the boy saw the cyclist equals the time in hours from when he first started, times his rate. Thus Pbc = Tbc * Rb

2. Supposedly, the boy passed the cyclest two hours after he passed the jogger. So Tbc = Tbj + 2

3. When the boy saw the jogger, he was 50 miles from point b. So Pbj = B - 50

4. The position of the boy when he saw the jogger equals his rate times the time it took to get there. Thus Pbj = Tbj * Rb

5. Supposedly, the girl saw the cyclist 20 minutes before she got 16 miles from point B. How long would it take her to get 16 miles frome point B? Well, Rg * T = (B - 16) T = (B - 16)/Rg. But she saw the cyclest 20 minutes before this time. We're working the problem in hours so thats 1/3 hour before. Thus Tgc = (B - 16)/Rg -1/3

6. Position of the girl when she saw the cyclist equals her rate, times the time it took her to get there. Thus Pgc = Rg * Tgc

7. We are told the girl met the jogger when she was 30 miles from be, thus Pgj = B - 30.

8. Position when girl saw the jogger equals her rate times the time it took to get there. Thus Pgj = Rg * Tgj

9. The cyclist drove from the position where he passed the boy, to the position where he passed the girl. So the distance he traveled between the 2 was (Pgc - Pbc). He did this from the time he passed the boy, to the time he passed the girl, and was driving at 8 mph. Thus the distance between the two also 8 * (Tgc - Tbc). These two distances are equal so (Pgc - Pbc) = 8 * (Tgc - Tbc)

10. The boy met the jogger 50 miles from B and the girl met the jogger 30 miles from B. Thus the positions where they met the jogger were 20 miles apart. Thus Pgj - Pbj = 20. (this is provable using equations 3 and 7)

11. The jogger traveled 20 miles from the position where he met the boy to the position where he met the girl. We don't know how long this was but we do know his rate was 6. So 6 * T = 20. T = 10/3. Thus The time from when the boy saw him to when the girl saw him was 10/3 hours. So Tgj - Tbj = 10/3. Rearraned Tgj = 10/3 + Tbj

12. Oops! I wrote this already. My bad!

Ok so thats 10 equations then. Not 11. 10 is just a combination of equations 3 and 7 (ironicly) so it doesn't count. And 12 I wrote already (in a rearranged form)

The equation may still be solvable at this point, with a lot of rearranging. But I'm going to see if I can find one last equation.