Question

Assume that one person can carry a four day supply of food and water for a trip across a desert that takes 6 days to cross. One person cannot make the trip alone because the food and water would be gone after 4 days. How many persons would have to start out in order for one person to get across and the others to return to the starting point?

Answer 1

google is your friend. Here is one solution of several:

https://www.algebra.com/algebra/homework/word/coins/Word_Problems_With_Coins.faq.question.775914.html

Answer 2

Have seen this in an old math book.

You start with 3 people.

At the end of first day, the 3 people now have 3 days' food each, one person give a days' food to the other two, so 2 people now have 4 days' food and the 1st has a days' food left and heads home.
At the end of day 2, the 2 people each have 3 days' food, so one gives a day's food to the other. Now, the one with 2 days' food heads home, and the one with 4 days' food has 4 days to get to the other side.

Answer 3

same source as mine
No page seems to have a valid algebraic solution.