Donkey eats carrot problem--New Ket/fei

A businessman rides a donkey to cross a 1000-kilometer-long desert and sells 3000 carrots. The donkey is known to carry 1000 carrots at a time, but eats 1 carrots every 1 kilometres. Q: How many carrots can a businessman sell?

A businessman rides a donkey to cross a 1000-kilometer-long desert and sells 3000 carrots. It is known that the donkey can carry 1000 carrots at a time, but eats 1 carrots every 1 kilometres. That's the problem.
Suppose there are 1000 of carrots in the desert, then there must be not more than 1000 before the desert, then at least two times before the desert, so from the point of departure to the edge of the desert there will be a round trip mileage, the distance will be more than 3000 kilometers away, so the final can sell the number of radish is less than 1000 root.
Then the total number of carrots will be exactly 1000 when you go to a certain location.
Since the donkey carries a maximum of 1000 at a time, the first place to unload the donkey is to make the number of Carrots 2000.
Because there are 3000 carrots at the beginning, the donkey must be carried three times, set the donkey to walk x kilometers for the first time to remove the radish
Then: 5x=1000 (the number of carrots eaten is also equal to the number of kilometres traveled)
x=200, which means only 200 kilometres for the first time.
Calculation: Donkey Pack 1000 walk 200 km left 800, remove 600, return to the departure point
The first two were hoarding 1200, the third without returning the remaining 800, then a total of 2000 carrots.
The second donkey only needs to carry two times, sets the donkey to walk y kilometer second time to remove the radish
Then: 3y=1000,y=333.3
Calculation: Donkey Pack 1000 walk 333.3 km left 667, remove 334, return to the first place to remove radish
The second time on the way will eat 334 radish, to the second time to remove the radish location is added 334, just 1000.
And then a total of gone: 200+333.3=533.3 km, and the remaining 466.7 km only need to eat 466 carrots
So the number of carrots that can be sold is 1000-466=534.

Donkey eats carrot problem--New Ket/fei