If a man and a half can dig a ditch and a half in a day and a half, how long does it take ten men to dig a ditch?
Answer:
Probably forever.
Re: Who needs algebra?
Posted: Sat Oct 11, 2014 12:04 pm
by DrStraw
Bill Spight wrote:Word problem:
If a man and a half can dig a ditch and a half in a day and a half, how long does it take ten men to dig a ditch?
It depends on how big the ditch is. If it is small then only one person can be in there digging at a time. If it is big they can all be in there digging together.
Re: Who needs algebra?
Posted: Sat Oct 11, 2014 1:12 pm
by Aidoneus
Bill Spight wrote:Actually, the fly has to go faster than the bicycles.
Yeah, you're right! Of course, the fly cannot go slower than the bike! Here is another, mathematically correct, though physiologically impossible, version of the anecdote (which is probably also apocryphal, http://www.math.ethz.ch/~efonn/stuff/anecdotes.html):
Two trains 200 miles apart are moving toward each other; each one is going at a speed of 50 miles per hour. A fly starting on the front of one of them flies back and forth between them at a rate of 75 miles per hour. It does this until the trains collide and crush the fly to death. What is the total distance the fly has flown?
The fly actually hits each train an infinite number of times before it gets crushed, and one could solve the problem the hard way with pencil and paper by summing an infinite series of distances. The easy way is as follows: Since the trains are 200 miles apart and each train is going 50 miles an hour, it takes 2 hours for the trains to collide. Therefore the fly was flying for two hours. Since the fly was flying at a rate of 75 miles per hour, the fly must have flown 150 miles. That's all there is to it.
When this problem was posed to John von Neumann, he immediately replied, "150 miles."
"It is very strange," said the poser, assuming the professor had immediately seen the simple solution, "but nearly everyone tries to sum the infinite series."
"What do you mean, strange?" asked Von Neumann. "That's how I did it!"
Re: Who needs algebra?
Posted: Sat Oct 11, 2014 1:34 pm
by Aidoneus
Bill Spight wrote:Word problem:
If a man and a half can dig a ditch and a half in a day and a half, how long does it take ten men to dig a ditch?
I think that is usually stated something like dig a "post hole" to avoid DrStraw's objection.
Moe, Larry, and Curly are painting your house. (Beware low bids.) Moe could finish the job alone in 4 hours, Larry alone in 3 hours, and Curly alone in 2 hours (he has a special bucket technique). They all start painting on different sides. However, while Moe and Larry are using red paint, Curly is using white paint. When will your house be all red?
1 house painted = T hours * (1 house/4 hours + 1 house/3 hours - 1 house/2 hours) => 1 house painted = 1 house * (T hours/12 hours) => 12 hour job. This or Three Stooges in a boat baling/boring often feature in my related rates algebra tests--instead of tanks simultaneously filling and draining.
Re: Who needs algebra?
Posted: Sat Oct 11, 2014 3:16 pm
by DrStraw
Aidoneus wrote:
Bill Spight wrote:Word problem:
If a man and a half can dig a ditch and a half in a day and a half, how long does it take ten men to dig a ditch?
I think that is usually stated something like dig a "post hole" to avoid DrStraw's objection.
That was not an objection. It was thinking outside the box, something most algebra students have trouble doing.
Re: Who needs algebra?
Posted: Sat Oct 11, 2014 5:10 pm
by cyclops
But then, you are a Dr !
Re: Who needs algebra?
Posted: Sat Oct 11, 2014 6:07 pm
by topazg
Bill Spight wrote:Word problem:
If a man and a half can dig a ditch and a half in a day and a half, how long does it take ten men to dig a ditch?
What on earth is half a man doing digging anyway?
Re: Who needs algebra?
Posted: Sat Oct 11, 2014 6:13 pm
by Aidoneus
topazg wrote:
Bill Spight wrote:Word problem:
If a man and a half can dig a ditch and a half in a day and a half, how long does it take ten men to dig a ditch?
What on earth is half a man doing digging anyway?
Don't you know that this is Walking Dead week?!
Edit: I'm sorry, I forgot that you are in England, so my "joke" may not have translated across the pond. Walking Dead is an American tv show about zombies, though almost half the lead actors seem to be British, like so many recent American cable shows or at least the better shows.
Posted: Sat Oct 11, 2014 7:12 pm
by EdLee
Word problem
There's probably a time and place for divergent thinking, for a punch line, for actual solutions, or for something else.
For example, given the word problem: an apple is on sale for $1 each; how much does it take to buy a dozen of them ?
Well, it depends on the context of the question, doesn't it.
If we're teaching children basic addition or multiplication, maybe there's an answer.
If I have some other agendas, I can come up with replies like, "Is there a volume discount for a dozen?", "Do I know the seller?", "Why is it on sale? Something wrong with it?", etc. The possibilities are practically limitless.
If the question is on the SAT or some other academic test which may affect your future, or if there's a reward of $1,000,000 for the "conventional" answer, then, you can still choose to give up your future or $1M to pay for your smart-ass reply.
Aidoneus wrote:almost half the lead actors seem to be British
The lead is definitely British, and his American accent is impeccable (at least to my ears). But I've only seen parts of season 1. Some day, I'll get a TV again.
Re:
Posted: Sat Oct 11, 2014 9:39 pm
by Aidoneus
EdLee wrote:
Aidoneus wrote:almost half the lead actors seem to be British
The lead is definitely British, and his American accent is impeccable (at least to my ears). But I've only seen parts of season 1. Some day, I'll get a TV again.
See http://klaq.com/how-many-walking-dead-a ... e-british/. I think that we are in the Golden Age for TV--cable TV, that is. Long-arc stories, with world-class actors and directors from around the world. My wife and I recently re-watched HBO's The Wire, and I still think that it is the best show ever.
Of course, the fly cannot go slower than the bike! Here is another, mathematically correct, though physiologically impossible, version of the anecdote (which is probably also apocryphal, http://www.math.ethz.ch/~efonn/stuff/anecdotes.html): 
