However, I think I have my own solution to the problem. I will post it very soon, once I have checked it

]]>I give up myself. I am not even interested in the solution that much. If it were a real world example or if the solution would provide some new insight then it would be worth the effort. But this is all starting to feel kind of like wasted time.

Good luck to you in this quest.

]]>Anyway, I was thinking about this problem a lot last night.

At any rate, maybe we should just keep cranking out rearragned forms and see if we find anything.

Pgj * Tgc = Pgc * Tgj = Rg

Pbj * Tbc = Pbc * Tbj = Rb

Pgj = 20 + Pbj

Tgj = Tbj + 10/3

hmm...

]]>I have since set the calculator on a quest to solve for Tbj, but it is now five minutes later and the TI is still only producing heat! ( I have since had to remove the batteries )

Take that for what it is worth. I still think that some other piece of information is needed. Maybe we are looking at this wrong. Would a final position of Jill in terms of variables be acceptable?

]]>I think that the crucial formula is for the time when the girl meets the cyclist. If you can solve for that time you would simply add 1/3 hour and know that it equals B - 16. I think that everything else would fall into place from there. I spent most of my time trying to solve for this time which I called t2.

I'm glad to atleast see that someone else has come up with the same relationships and that I am not crazy.

Notice that Tgc = f(Rg,Tbj) = f(Rb,Tbj) = f(B,Tbj), which become very large expansions.

Taking two of my large functions for Tgc and subtracting one from the other resulted in:

where x = B (total distance) and y = Tbj (or t1) ; I got this mess;

51x²y - 27x² + 48x²y² + 9x²y^3 - 2606xy + 1200x - 2080xy²....

-96xy³ + 72xy^4 + 5680y - 1600y² - 17700y³ - 3600y^4 - 11700 = 0

Now you **may** want to use the quadratic equation to solve for B, but I can't imagine the answer providing anything that humans would want to read.

If you like putting things like this into electronics devices then by all means go ahead.

]]>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.

]]>*Two walkers Jack and Jill walked by the same road and at the same time from point A to point B. When Jack was 50 miles from point B, he passed a jogger who was jogging towards point B at 6 miles per hour. Two hours later, Jack met a cyclist going in the opposite direction at 8 miles per hour.*

When it says 2 hours later, does it mean two hours after they first started walking? Or two hours after he passed the jogger?

]]>I will try to get my drawings on the other problem as well. I am almost sure that it was just a two dimensional solution.

]]>I know exactly how you feel, I have spent a long time on this also to no avail. However, I am only 17, so I thought that I would open it up to the more qualified mathematicians on here who may have been able to offer an approach I wasn't familiar with.

this doesn't sound like a particularly great question

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