SOLUTION: A person decides to walk, across a desert, without assistance and alone. The desert is entirely without resources. The trail is 100 kilometers in length, and at every 20 km. is a

Question 1171942: A person decides to walk, across a desert, without assistance and alone. The desert is entirely without resources. The trail is 100 kilometers in length, and at every 20 km. is a shelter. A person can walk 20 km. per day. The person can only carry food for 3 days, and food can only be kept at shelters.
Determine length of time (days) to cross the desert.
Not sure how to solve.
Answer by Solver92311(821) (Show Source): You can put this solution on YOUR website!

Assumption 1: There is unlimited food available at kilometer 0.

Assumption 2: There is food available at kilometer 100.

Assumption 3: There is no food at any of the intermediate shelters, i.e. at km 20, km 40, km 60, or km 80.

It is clear that if you had 3 days of food staged at km 40, you could get to the end in 3 days starting at km 40. One day to 60, one day to 80, and one day to 100.

It takes 2 days to move one day of food from one shelter to the next and get back to get more food but it is only possible to do that if you start with 3 days of food in the first place.

Starting at the beginning, you can stage one day of food at 20 in 2 days ending at the start again, then in 2 more days, you can stage the second day of food at 20, and so on.

If you do this 4 times (taking 8 days) you will have four days of food staged at 20 and be at the start. You pick up 3 more days of food and go to 20. You will now have 6 days of food at 20 in one day. 9 days used.

You take 3 days of food from 20, go to 40, drop one day of food and go back to 20. 11 days used

You take 3 more days of food, go to 40, using 1 day for a total of 12 and you will be at 40 with 3 days of food.

Three more days for a total of 15 and you are at the destination.

John

My calculator said it, I believe it, that settles it

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