Deep into the desert

Four travelers once decided to explore a wild, barren desert. They knew they wouldn’t be able to find any water along the way. Therefore, in addition to the necessary equipment and food, everyone had to bring a supply of drinking water. Each person could carry enough water and food for only 10 days—no more. And if they all went together, they wouldn’t be able to venture deeper into the desert than five days’ journey. However, if, say, after a day or two, one of the four were to keep only what was necessary for the return trip and give the remaining provisions to his companions, the other three could proceed farther than five days’ journey.

It was important for the travelers to penetrate as far as possible into the desert. To do this, the final day’s march had to be undertaken by a single person.

Assuming that the transfer of food and water—and, if necessary, the establishment of securely hidden food caches—took place only at the end of each day’s stage, how far into the desert could one of the travelers have advanced?