A researcher wants to cross the desert to the nearest oasis, 380 km away, with the help of two porters. They can travel 60 km per day, and both the researcher and the porters can carry enough food and water for a maximum of four days. The researcher must ensure that the porters can return to where they started from. Food and water cannot be stored in the desert.

Can the researcher cross the desert under these conditions, without counting on any help arriving at the destination?
We consider that both food and water decrease proportionally over time, meaning that neither the researcher nor the porters can proceed if their food runs out. Thus, with four days' worth of food, the researcher can travel a maximum of $4 \cdot 60 = 240 \text{ km}$. Therefore, after traveling $380 - 240 = 140 \text{ km}$, the researcher must have four days' worth of food.

If the porters' schedule is optimally organized, when any porter turns back, those heading towards the oasis must carry a full load. Otherwise, the porter could turn back earlier, and the achievable distance would remain unchanged.

Thus, we start as follows: all three individuals set out fully equipped. After some time, one porter transfers enough food to the other two so that they each have four days' worth of food again, and he turns back. This means that the porter travels with the others for exactly one day. During this time, each of them consumes one day's worth of food. The one who turns back transfers 1 day's worth of food and returns to the oasis with the remaining one day's worth of food.

![](https://cdn.mathpix.com/cropped/2024_05_02_c5b7ad93d4fb7a117cfbg-1.jpg?height=626&width=829&top_left_y=619&top_left_x=645)

With this, they have already traveled 60 km out of the 380 km. According to our previous observation, the researcher and the porter still need to travel $140 - 60 = 80 \text{ km}$. During this time, they consume $4 / 3$ days' worth of food. The porter replenishes the researcher's food supply, leaving him with $4 - 4 / 3 - 4 / 3 = 4 / 3$ days' worth of food, and he needs to return to the starting point with this. But now he has $21 / 3$ days' worth of travel left! How can he still return? After the first porter returns, he can turn around again and rush to his companion. His companion will run out of food in $22 / 3$ days, so if the first porter rushes ahead with 3 days' worth of food after a $2 / 3$ day rest, both will return, and their food will run out exactly when they arrive home.

The researcher's journey is illustrated in the diagram.

Thus, the researcher can cross the oasis.

Note. If the schedule is further optimized, with appropriate timing, the researcher can reach $3862 / 3 \text{ km}$.