Author |
Message |
Merrysea
Member
08-13-2004
| Sunday, December 03, 2006 - 1:38 pm
My DS3 is in calculus, and they have an algebra problem that no one in the class can solve, so I'm hoping to get some input here. (Hint: The answer is not zero.) The problem is: Martin the Mule works for the owner of a small, remote pineapple plantation. This year's harvest consists of 3,000 pineapples. Marty can carry up to 1,000 pineapples at a time. The marketplace where the pineapples are sold is 1,000 miles away. Unfortunately, Marty eats one pineapple each and every mile he walks. Of the 3,000 pineapples harvested, what is the largest number of pineapples Marty can get to market?
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Kitt
Member
09-06-2000
| Sunday, December 03, 2006 - 1:49 pm
Is he allowed to stop part of the way? For example he could take 1000 pineapples half way and leave 500 there, return home, get 1000 more walk 500 miles, pick up the 500 he left (add them to the 500 he has now) and now he can carry that new 1000 the 500 miles and have 500 left at the end of it. (That ignores the third 1000.) There should be someway to maximise that with the 3000 pineapples.
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Seamonkey
Moderator
09-07-2000
| Sunday, December 03, 2006 - 1:57 pm
Or just call Fedex.. I guess he'd eat one before the first mile?
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Merrysea
Member
08-13-2004
| Sunday, December 03, 2006 - 2:18 pm
My son's assumption is that he will eat one pineapple after each mile he walks, both there and back.
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Kitt
Member
09-06-2000
| Sunday, December 03, 2006 - 2:24 pm
Assuming the mule is allowed to stop part way along and return to restock I think the answer's 833. He wants to minimise the number of times he ever has to travel a portion of the trip (as the more times he travels the more pineapples he eats), so he needs to take as much as he can (1000 pineapples) each time he takes a trip. In his first batch of trips he wants to take the three batches of 1000 far enough so that he will have 2000 left: So trip one he takes 1000 pineapples 333 miles, leaving 667 at that point. Trip two as above. Trip three as above. He now has 667 x 3 = 2001 pineapples at the 333 mark. In his second batch of trips he wants to take the two batches of 1000 far enough so that he will have 1000 left: Trip four takes 1000 pineapples 500 miles, leaving 500 at the 833 mile point. Trip five as above. He now has 1000 pineapples at mile 833. In the last trip he takes the 1000 pineapples the last 167 miles, eating 167 and getting 833 to market.
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Kitt
Member
09-06-2000
| Sunday, December 03, 2006 - 2:27 pm
Argg don't say that! In that case he'd never get any pineapples to market. I think we have to assume if the mule's not carrying any pineapples he doesn't eat any (and doesn't die!). It's the only way to get a non-zero answer. (Got to go and put up the Christmas decorations - good luck!)
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Seamonkey
Moderator
09-07-2000
| Sunday, December 03, 2006 - 3:19 pm
Hmm but each and every would be loaded or unloaded, no?
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Kitt
Member
09-06-2000
| Sunday, December 03, 2006 - 10:48 pm
Please let me know if you find out the correct answer (or get more clarity on the question)!
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Kitt
Member
09-06-2000
| Sunday, December 03, 2006 - 11:39 pm
Just in case the mule has to eat pineapples on the way back too: Same logic, but you have to double the pineapples eaten on every trip except the last one in each section. Trips 1-3: Take 1000 pineapples 200 miles and walk back (using 400 pineapples and leaving 600 at the 200 mile marker). Take 1000 pineapples 200 miles and walk back (using 400 pineapples and leaving 600 at the 200 mile marker). Take 1000 pineapples 200 miles with no need to walk back (using 200 pineapples and leaving 800 at the 200 mile marker). He now has 2000 pineapples at the 200 mile marker. Trips 4+5 Take 1000 pineapples 333 miles and walk back to the 200 mile marker (using 666 pineapples and leaving 334 at the 533 mile marker) Take 1000 pineapples 333 miles with no need to walk back (using 333 pineapples and leaving 667 at the 533 mile marker) He now has 1001 pineapples at the 533 mile marker. Trip 6 Take the 1000 pineapples the 467 miles to market, eating 467 and leaving 533 to sell.
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Zachsmom
Member
07-13-2000
| Monday, December 04, 2006 - 6:32 am
Answer: Don't walk behind the mule.
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Merrysea
Member
08-13-2004
| Monday, December 04, 2006 - 6:59 am
He should find out the answer today - I'll let you know as soon as I do! Kitt, thanks for all your help!
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Scooterrific
Member
07-08-2005
| Monday, December 04, 2006 - 7:03 am
<-----------Runs for her life slamming door behind her.
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Cndeariso
Member
06-28-2004
| Monday, December 04, 2006 - 7:24 am
i'll ask my husband. he taught high school math.
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Cinnamongirl
Member
01-10-2001
| Monday, December 04, 2006 - 2:57 pm
I think 400
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Cinnamongirl
Member
01-10-2001
| Monday, December 04, 2006 - 3:17 pm
-1st trip out takes 1000.. goes 400 miles leaves 200 there an goes the 400 miles back.. eating (400+400) 800 for the trip -2nd trip same -third trip he takes the last 1000, eating 400 to get the 400 miles, pickes up the (200+200) 400 he left the first two trips, now he has 1000 and eats 600 during the last 600 miles leaving 400 at the end!!! each trip was two ways, cept the third which was only one way because he didnt need to go back and he could only carry 1000 for the last trip, (to the market) So take the rest (2000) and divided it by 5 (the number of initial legs) (2 each of two trips and 1 of one trip) that gave 400.. so 400 out and back twice, leaving 200 pineapples each time, and the last trip where he would still have 600 when he'd reached the 800 he'd left
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Cndeariso
Member
06-28-2004
| Monday, December 04, 2006 - 3:27 pm
how do we know he is making these stops? my dh asked what the assumptions were for this problem as there don't seem to be any. so, are we supposed to make our own and come up with an answer as long as we can defend it?
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Merrysea
Member
08-13-2004
| Monday, December 04, 2006 - 4:05 pm
Well, the teacher didn't give them the answer today. The majority of kids came up with 500, one got 533 1/3, and one got 625.
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Ophiliasgrandma
Member
09-04-2001
| Monday, December 04, 2006 - 4:14 pm
Mules don't eat pineapples.
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Kitt
Member
09-06-2000
| Monday, December 04, 2006 - 7:24 pm
Yeah, OG, maybe it was a trick question afterall 
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Shashakaye
Member
05-19-2003
| Tuesday, December 05, 2006 - 10:36 am
Maybe Martin the mule and Marty aren't the same person. Martin is the mule & Marty is the plantation owner. If Marty can carry 1000 pineapples, Martin can carry the rest. I guess the answer would then be 2000.
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Hermione69
Member
07-24-2002
| Tuesday, December 05, 2006 - 1:05 pm
3
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Hukdonreality
Member
09-29-2003
| Tuesday, December 05, 2006 - 1:10 pm
I think he walks 999 miles and eats 999 pineapples, leaving 1 at the 1 mile mark. He repeats this 2 more times. On his third trip, he picks up the two he'd left previously, and eats the one he had left from his last trip. He delivers 2. Then Marty is shot by the plantation owner.
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Scooterrific
Member
07-08-2005
| Tuesday, December 05, 2006 - 1:17 pm
This season Marty's hungry...so he eats the pineapples before leaving, because he knows how many miles it is, because the dadgum plantation owner is too cheap to buy another flippin mule to help carry the load. After he eats his thousand pineapples in one sitting, he needs a nap. He lays down to take a nap and his stomach explodes and Marty is no more.
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Native_texan
Member
08-24-2004
| Tuesday, December 05, 2006 - 1:18 pm
Zero
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Hukdonreality
Member
09-29-2003
| Tuesday, December 05, 2006 - 2:02 pm
Maybe Marty can only carry 1,000 pineapples, and he'll have to eat one every mile...BUT, what if Marty can drag the other 2,000 behind him? Then he'd deliver 2,000. Then Marty would not have to be shot
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