An Explorer needed to make a 5 day trip across a dessert. Each man with him could carry exactly 3 days food and water. For one man how many men will it take to cross the dessert?

My name is Zach. I am in the eighth grade.

Thank you

Well, if she is alone and there are no lions in that desert, she can proceed as follows:

First she takes three bags of supplies, carries them on a one-day hike (eating from the first bag on the way), then leaves the second bag at the first campsite and walks back the next day eating from the third bag.

On the third day, she sets out for an identical journey, so she comes back at the end of the fourth day and there are now 2 bags of food waiting at the first campsite (and no lion will eat them).

On the fifth day, she again sets out for an identical trip. Thus at the end of the sixth day, there are three extra bags of food at the first campsite.

On the seventh day, she sets out for a four-day trip: As she arrives at the first campsite at the end of one day, she is carrying two bags of food with her and there are three extra bags there. On the next day, she takes three bags along and sets out for the second campsite. She will come back to the first camp site at the end of the next day, having left one bag of food at the second campsite. She now needs to take one bag of food for the walk back home. By then, there is a bag of food at the first campsite and another one at the second campsite.

Therefore on the tenth day, the explorer is ready to start her treck across the desert. Starting with three days of food, she will eat one during that day, but then she will be able to replace it with the one from the first campsite. The next day, she will again eat a bag of food, which she will replace by the one from the second campsite. She will then have three bags of food and three more days of walking ahead, so she will make it and arrive on the other side at the end ot the fifteenth day.

In this way, it takes fifteen days (and fifteen bags of food) for one person to get across the desert. With helpers, it can be done in a shorter time because they can share tasks. Can you see how? Remember that these helpers will be walking back instead of going across the desert.