This year's harvest from a small, remote banana plantation consists of 3000 bananas. The farmer's camel can carry up to 1000 bananas at a time. The market where the bananas are sold is 1000 miles away. Unfortunately, the camel eats one banana each and every mile she walks. Of the 3000 bananas harvested, what is the greatest number of bananas the farmer can get to market?
(*The answer is NOT zero bananas. *If the camel is carrying bananas, she eats bananas. *If the camel is returning and NOT carrying bananas, she eats NOTHING. *The camel can go partway to the market and drop off bananas and return for another load. The camel can also pick those bananas up later. Any bananas dropped off will be there later to be picked (noone will steal them). *The camel can only travel in full miles (no half miles).) HINTS: 1.Use something to represent the camel and physically move it and record carrying and drop offs. 2.Keep a record of everything you tried. 3.Write up steps when you have the answer to deescribe the trip. GOAL: To finfd the MOST amount of bananas that will make it to market.
To find the greatest number of bananas the farmer can get to the market, we can use a step-by-step approach and keep track of the number of bananas with the farmer and the camel at each stage of the journey.
Step 1: The farmer and the camel start at the plantation with 3000 bananas.
Step 2: The camel carries a maximum of 1000 bananas and walks 1 mile, eating one banana along the way. The remaining bananas with the camel are 999.
Step 3: The camel continues walking and reaches the first drop-off point after 1000 miles. The remaining bananas with the camel are still 999.
Step 4: The camel drops off all the bananas at the first drop-off point and heads back towards the plantation with an empty load, eating no bananas during the return journey.
Step 5: The camel reaches the plantation after walking 1000 miles and no bananas are eaten during the return journey.
Step 6: The camel picks up 1000 bananas from the plantation and starts the second trip towards the first drop-off point.
Step 7: During the second trip, the camel walks 999 miles while eating one banana for each mile. The remaining bananas with the camel are 1.
Step 8: The camel reaches the first drop-off point with 1 banana.
Step 9: The camel drops off the single banana at the first drop-off point and heads back towards the plantation with an empty load, eating no bananas during the return journey.
Step 10: The camel reaches the plantation after walking 999 miles and no bananas are eaten during the return journey.
Step 11: The camel picks up the remaining 1000 bananas from the plantation and starts the final trip towards the first drop-off point.
Step 12: During the final trip, the camel walks 999 miles while eating one banana for each mile. The remaining bananas with the camel are 1.
Step 13: The camel reaches the first drop-off point with 1 banana.
In total, the farmer can get 1000 + 1 + 1 = 1002 bananas to the market.