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.
I am assuming that the thought process here is for one or more of the motorbikes to tow some subset of the others to extend the range past the 100 mile limit they would all have if they merely started together.
For example, if one bike towed Darren's bike, logic and physics would dictate that the resistance of the two together would be double that of a single bike, resulting in a 50 mile range for the combined two bikes. (I am ignoring the minor mass vs. distance effect of using up the fuel of one bike towing another, vs. one bike using up its own fuel, which could in theory make a small difference). When the towing bike ran out of fuel at 50 miles, Darren's bike would still have 100 miles of range, allowing for a total range of 150 miles.
Combining this thought process in some way using all 16 bikes will generate the optimal answer, I believe.
Another thought is to stage the bikes and transfer fuel, however, having any two bikes driven to the same point seems like a waste of fuel. I could be wrong.
Edited on December 27, 2022, 8:13 am
Edited on December 27, 2022, 8:20 am
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Posted by Kenny M
on 2022-12-27 07:01:53 |
A start - (no solution)
