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Car Talk Puzzler: The Endless Mile
Posted: Tue May 06, 2008 2:31 pm
by MarleysGh0st
This week's Car Talk Puzzler is another math problem, which I always find amusing.
This Week's Car Talk Puzzler:
The Endless Mile
RAY: This was sent in by John Kelly and he writes with a true story:
"While living in the Bronx a friend, who will remain anonymous, bought a car in White Plains about 21 miles north of the city. He didn't have anyone to help him pick it up so he decided to do it all by himself." (Now whenever someone says, "a friend who will remain anonymous," and then the rest of the story is something harebrained, you know it's him! So John, we're with you, brother!)
"And because he wasn't trading the car in, he came up with this ingenious plan.
He drove his old car 21 miles north and parked it in the dealer's lot, picked up the new car, paid for it and got the keys, and drove it one mile south. He locked it up, walked back north one mile to the dealer, picked up his old car drove it two miles. He locked it up, walked back one mile, picked up the new car, drove it two miles south, locked it up, walked one mile back to the other car, etc., etc., etc., until he reached home with both cars."
So the question is, at the end of the very long, long day, how many total miles did he walk and drive? Sounds simple, right, but be careful!
Think you know the answer?
Drop us a note!
Once you figure out your answer, take a moment to consider if John came up with an optimal solution or not!
Posted: Tue May 06, 2008 3:01 pm
by Bob Juch
He drove 63 miles and walked 21 miles. He could have just walked to the dealer and driven his new car 21 miles back.
Posted: Tue May 06, 2008 3:11 pm
by bazodee
Hmm... drove 63 and walked 22.
Posted: Tue May 06, 2008 3:12 pm
by slam
Problems like this are easy if you don't get bogged down in the details. His new car needs to travel the 21 miles from the dealership to his home. His old car needs to go 21 miles each way for a total of 42 miles. He needs to walk the same 21 miles (he never doubles back on himself). So, the total is 63 driving and 21 walking miles.
This is far from the optimal solution. He could save 42 driving miles and with gas approaching $10/gallon, that's rather wasteful!
Posted: Wed May 07, 2008 10:45 am
by megaaddict
I think Tom and Ray owe it to poor John to discuss a little "train talk" in the context of this puzzler.
Posted: Wed May 07, 2008 11:12 am
by MarleysGh0st
megaaddict wrote:I think Tom and Ray owe it to poor John to discuss a little "train talk" in the context of this puzzler.
Yeah, well, I think it was implicit in the problem that "no friends available to give him a ride" also meant "no public transportation."
Re: Car Talk Puzzler: The Endless Mile
Posted: Wed May 07, 2008 4:13 pm
by etaoin22
MarleysGh0st wrote:This week's Car Talk Puzzler is another math problem, which I always find amusing.
This Week's Car Talk Puzzler:
The Endless Mile
RAY: This was sent in by John Kelly and he writes with a true story:
"While living in the Bronx a friend, who will remain anonymous, bought a car in White Plains about 21 miles north of the city. He didn't have anyone to help him pick it up so he decided to do it all by himself." (Now whenever someone says, "a friend who will remain anonymous," and then the rest of the story is something harebrained, you know it's him! So John, we're with you, brother!)
"And because he wasn't trading the car in, he came up with this ingenious plan.
He drove his old car 21 miles north and parked it in the dealer's lot, picked up the new car, paid for it and got the keys, and drove it one mile south. He locked it up, walked back north one mile to the dealer, picked up his old car drove it two miles. He locked it up, walked back one mile, picked up the new car, drove it two miles south, locked it up, walked one mile back to the other car, etc., etc., etc., until he reached home with both cars."
So the question is, at the end of the very long, long day, how many total miles did he walk and drive? Sounds simple, right, but be careful!
Think you know the answer?
Drop us a note!
Once you figure out your answer, take a moment to consider if John came up with an optimal solution or not!
Seems to me he has to walk 21 miles, just as if he decided to walk all at once to White Plains, his old car goes 42 and the new one goes 21.
Total, 21 walk, 63 drive. I am trying to think if I am missing a fillip at the end which changes the result, but I cant see it/