Problem 2

## Crossing The Desert

A traveler undertakes to walk, alone and without help, across a desert entirely lacking in resources. Every 20 kilometers on the 100 kilometer trail there is a shelter. (20 kilometers is exactly what a traveler can walk in one day.) The traveler can only carry 3 days' food. He can stock food only in shelters. How many days will it take him to cross the desert? — Mr. Simmons

Ok, so the traveler apparently has to travel 100 km and can stop every 20 to stock food at shelters. in order to have enough food, he has to stock up enough at the first 2 shelters to make it across the desert. so at first, he has to stock up 5 days worth of food at the first shelter. this takes him 9 days as he has 1 days worth for the trip to the shelter, leaves 1 there, and consumes the rest on the way back. then, he takes 3 of the 5 days worth, travels to the second shelter, and leaves 1 there. (the other 2 are consumed on the way there and back) .10 days have passed. lastly, he goes back to the first, gets the last 2 days worth, and ends up with 3 days worth of food at the second shelter (12 days). with that, he continues on a 3 day journey to the finish. so the grand total would be 15 days.

-Rafa R

Wowie! okay…. i agree with rafael! yay! At first all those words confused me so I decided to draw a little diagram.
*start* --|---|----|---—|---—| *end*
The diagram represents the distance he is going to travel. Each line marks a 20 km distance - where each shelter is located. I tested rafael's process and i found that it worked. So I agree with Rafael and my answers is 15 days as well. :D
~ shreeya

page revision: 84, last edited: 16 May 2009 21:45