hiijacker-
Full solution, with explanation and numbers for each step:
Until we get down to 2,000 bananas, five bananas will be consumed for each mile traveled, since each mile requires three trips forward and two back. This also gives up 200 total miles traveled from the starting point (1,000 miles divided by five trips).
We are now down to 2,000 bananas remaining, which means we only need three miles traveled for each mile of actual progress. We will divide the 1,000 bananas by three (for the number of trips needed until there are only 1,000 bananas left).
This results in 333 (bananas or miles).
The camel will travel another 333 miles (to the 533 mile-mark) with a load of 1,000 bananas, return with another 333 that it eats on the way, then pick up the last 1,000 bananas and return to the 533 mile mark while eating another 333.
The camel is now at the 533 mile marker with 1,001 bananas.
The camel is loaded with 1,000 bananas and fed the remaining banana.
It then proceeds the last 467 miles, eating one additional banana for each mile after the first one.
He gets to marked with 534 bananas, and one very well-fed camel.