Darren has 16 motorbikes with a tank that has a capacity to go 100 miles (when the tank is full).
→ All the motorbikes are initially fully fueled.
→ Each start from the same point.
→ Each bike has a rider on it.
Using these 16 motorbikes optimally, determine the maximum distance that Darren can travel.
Note:
It is not necessary for all the bikers to reach at that final point.
As D2, this seems to be a research problem. Starting with a search for the rocket equation, which seems similar, I was finally led to the Jeep Caravan Problem
a paper by Margaret Carpenter (2016), who references the work of CJ [or C.G. per the bibliography] Phipps from 1947.
Down to the nitty-gritty:
If c is the capacity in mile-equivalent fuel of one Jeep (in our problem, motorcycle), and m is the number of such vehicles, the distance that can be traveled is
c + c/2 + c/3 + ... + c/m
apparently achieved by transferring fuel from one tank to be shared among all the rest as soon as that would bring all of those to a full tank, happening at even intervals along the way.
c=100; dist=sym(0);
for i=1:16
dist=dist+c/i;
end
dist
disp(eval(dist))
finds
dist =
12182795/36036
or 338.072899322899
to be overly precise, but, hey, this is a puzzle, where everything is perfect. But 338 miles would be a good answer.
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Posted by Charlie
on 2022-12-27 10:40:38 |
researched solution
