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

Does the traveler have to spend a day to stock the food? If so, 7 days. If not, I think it would be 5 days because you walk 20 km to the first shelter, stock up, go for 3 days that you are carrying with you, and then finish the 100 km on the last day. But does he start with food for 3 days? I don't think so but if so, it would only take him 5 days as well.
-Courtney W.

My question is if the traveler starts out with food… and Courtney, isn't the total distance 100 km? (or am I wrong?) Either way, I think it would take 5 days. Ignoring all the other information, since the traveler can only walk 20 km per day, and there's 100 km, it would take 5 days. (Will need to think of other ways to solve this), but this is my answer for now.
-Jane L.

Yea I think it is 5 days becaus he only needs to stock for food once. And that lasts three days, and then there is one day at the begining and one at the end for a total of 5 days.

~Maha A.

Oh wait… I just reread the problem and he has to stock the food himself -"He can stock food only in shelters" so theres not already food in the shelters for him to take… that probably makes it alot more.

~Maha A.

If Maha is right, then I think it would be 9 days because he goes with 3 days worth of food, loses a day to go to the 1st shelter, leaves a day worth at the shelter, and uses another day to get back. 2 days. Then he goes again, wasting 2 days, but having 2 stored now. Then he goes again, but now he has food for 4 days, the rest of the journey. So he uses 5 days to get the food he needs, and 4 days to get the rest of the way.. so I change my answer to 9 days! Because it goes like this:

Day 1-go to the first shelter, store a day's of food, eat +20 km
D2-go back, eat food, stock another 3 days of food -20 km
D3-go to the 1st shelter again and store 1 day of food, eat +20 km
D4-go back, eat food, stock -20 km
D5- go to the first shelter, where you have 2 days of food, combined with your 2 days of food you didn't eat on the way=4 days of food +20 km
D6-9-eat and travel 20 km +80 km

-Courtney W.

Yeah thats what I think. You gotta stock food, go back get 3 days of food again, go to next shelter thingy…etc.
And also according to the question…there's a shelter at the very end of the desert. WHY WOULD U NEED ONE THERE??? am i right? Can someone tell me? thanks :)

~~~~~ Harsha R. :)

Ok, I'm thinking that it will take 15 days:
Day 1,2 : Go to 20 km shelter, store food for one day, go back to starting point (0 km)
Day 3,4 : repeat as day 1,2 (0 km)
Day 5,6 : repeat but stop at 20 km
Day 7,8 : At 20 km, pick up one day's food, go to 40 km
Day 9,10 : Go back to 20 km, pick one day's food, back at 0 km
Day 11, 12 : Get 3 day's worth food, go to 20 km (first shelter), get one day's worth food, go to 40 km, get 3 day's worth food
Day 13, 14 : Go to 60 km, and then 80 km
Day 15 : Arrive at 100 km

-Jane L. :)

wow.. this is late reply (kinda?) but yea i think its 15 days too. ill post the explanation later… very sleepy right now. D:
-Sai Aparna K.

Or the dude could just starve 2 of the days and then get through in 5 days… But i guess you guys are all agreeing with 15 days? And Jane, why did it take 2 days (day 7 and 8) to go from 20km to 40km? shouldn't that take 1 day?

— _ — _ — _ — Rob C.

page revision: 90, last edited: 10 May 2009 15:17