Fraser decides to start small and figure out how many bananas the camel can carry 1km. If the camel carried 1000 bananas at a time, it would have to make three trips to transport the entire pile. During these trips, the camel would consume five bananas (three when moving forward and two to return to the pile). Therefore, it will take the camel five bananas to move 1km. By using this formula, the camel would only get 600km across the desert before it ran out of bananas (1000/5 = 600). BUT, the number of trips decreases as the number of bananas decreases.
To travel 200km, the camel will eat 1000 bananas. So, at 200km across the desert, the camel is left with 2000 bananas (3000-1000 = 2000). At this point, the camel will eat three bananas per km it travels (two trips moving forward with 1000 bananas at a time and one trip back to collect more bananas).
The camel will be able to travel another 333km before it's down to 1000 bananas.* When the camel is down to 1000 bananas, it will have traveled a total of 533km (200 + 333 = 533). Now the camel can carry all of the remaining bananas and travel the final 467km across the desert, arriving with 533 bananas (1000-467).
*At this point, the camel will actually have 333 and 1/3 bananas left. Fraser leaves the third of the banana to rot in the sun. But if you were to calculate this partial banana into the formula, the camel would be able to carry a total of 533 and 1/3 bananas across the desert.Submitted 6/22/2001 10:22:02 PM