MathStudent1999
Junior Member
- Joined
- Mar 18, 2012
- Messages
- 76
Can someone help me on this word problem?
There is a farmer who has 3000 bananas. He wants to sell them at a market 1000 miles away. The only way to get to the market, from his farm, is by camel. The farmer's camel can only carry 1000 bananas at a time. However, the camel is very hungry and needs to eat a banana every mile it travels, to refuel. What is the most amount of bananas the farmer can get to the market?
Since the farmer cannot go all the way to the market and still have bananas to sell, the only way he can get bananas to the market would to drop bananas in the middle of the route between his farm and the market. Then he would need to go back to his farm and get some more bananas.
The farm|_|_|_|_|The market.
The most bananas I could get to the market was 501 bananas. I split the route into 4 sections. The farmer would take 1000 bananas, go to the first seperator and drop-off 500 bananas before returning to the farm. From the farm, he would pickup another 1000 bananas. He the would go to the first separator and pickup 250 bananas so he would still have 1000 bananas on him. He would then go to the second separator, drop-off 250 bananas before returning to his farm. He would then pickup the last 1000 bananas and go to the first and second separators, pickup the remaining 250 bananas from each. That leaves him with 1000 bananas at the second separator. Going to the third separator, and then the market, the camel would need to eat 500 bananas. By not feeding the camel when the farmer arrived at the market, he can gain a extra banana. That leaves the farmer with 501 bananas at the market.
501 was the most I could get, but I cannot prove it is the most. Could someone show me how to prove this is the most, or prove that another number is the most.
Thank You.
There is a farmer who has 3000 bananas. He wants to sell them at a market 1000 miles away. The only way to get to the market, from his farm, is by camel. The farmer's camel can only carry 1000 bananas at a time. However, the camel is very hungry and needs to eat a banana every mile it travels, to refuel. What is the most amount of bananas the farmer can get to the market?
Since the farmer cannot go all the way to the market and still have bananas to sell, the only way he can get bananas to the market would to drop bananas in the middle of the route between his farm and the market. Then he would need to go back to his farm and get some more bananas.
The farm|_|_|_|_|The market.
The most bananas I could get to the market was 501 bananas. I split the route into 4 sections. The farmer would take 1000 bananas, go to the first seperator and drop-off 500 bananas before returning to the farm. From the farm, he would pickup another 1000 bananas. He the would go to the first separator and pickup 250 bananas so he would still have 1000 bananas on him. He would then go to the second separator, drop-off 250 bananas before returning to his farm. He would then pickup the last 1000 bananas and go to the first and second separators, pickup the remaining 250 bananas from each. That leaves him with 1000 bananas at the second separator. Going to the third separator, and then the market, the camel would need to eat 500 bananas. By not feeding the camel when the farmer arrived at the market, he can gain a extra banana. That leaves the farmer with 501 bananas at the market.
501 was the most I could get, but I cannot prove it is the most. Could someone show me how to prove this is the most, or prove that another number is the most.
Thank You.