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Math problem: Who is correct, The Teacher or The Student?

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Actually, both 15 and 20 would be correct.

Let's assume that the board is of some arbitrary size, like 10"x10". The cutter is using a handsaw that can cut at the rate of 1"/min.

The cutter cuts through the middle of the board, you have 2 pieces that are 5"x10", and it takes 10 minutes.

If the cutter wants three pieces there are two options:
1) The cutter cuts off one third of the board. It is a 10" cut that takes 10 minutes and the cutter now has a 3.3"x10" piece and a 6.7"x10" piece. The cutter then cuts the larger piece in half the long way, which is a 10" cut and takes 10 minutes. The cutter now has three boards that are 3.3"x10" and it took 20 minutes to get them.
2) The cutter cuts the board in half. It is a 10" cut that takes 10 minutes and the cutter now has two pieces that are 5"x10". The cutter then cuts one piece in half the short way, which is a 5" cut and takes 5 minutes. The cutter now has one board that is 5"x10" and two boards that are 5"x5" and it took 15 minutes to get them.

So, really, both answers are theoretically right. The problem is, as usual, that pattern recognition problems often lack sufficient information to isolate one, and only one, plausible pattern.
 
DrPizza said:
Well duh, the new board is 12"x12". The first cut is 12" long. But the second cut is only 6" long.
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and
sactoking said:
Actually, both 15 and 20 would be correct.

Let's assume that the board is of some arbitrary size, like 10"x10". The cutter is using a handsaw that can cut at the rate of 1"/min.

The cutter cuts through the middle of the board, you have 2 pieces that are 5"x10", and it takes 10 minutes.

If the cutter wants three pieces there are two options:
1) The cutter cuts off one third of the board. It is a 10" cut that takes 10 minutes and the cutter now has a 3.3"x10" piece and a 6.7"x10" piece. The cutter then cuts the larger piece in half the long way, which is a 10" cut and takes 10 minutes. The cutter now has three boards that are 3.3"x10" and it took 20 minutes to get them.
2) The cutter cuts the board in half. It is a 10" cut that takes 10 minutes and the cutter now has two pieces that are 5"x10". The cutter then cuts one piece in half the short way, which is a 5" cut and takes 5 minutes. The cutter now has one board that is 5"x10" and two boards that are 5"x5" and it took 15 minutes to get them.

So, really, both answers are theoretically right. The problem is, as usual, that pattern recognition problems often lack sufficient information to isolate one, and only one, plausible pattern.
Click to expand...


Bingo. Cool math problem. Wrong teacher for saying there is only one answer.

We ASSUME that the 3 boards need to be of same dimensions. Like Dr. Pizza says, I could take a square board, cut it in half and then divide half again. That second cut will be shorter in length.

in fact, I can make 3 pieces in 11 minutes.
1. cut square board near the edge so that you have a rod (10 min)
2. cut the rod (<1 min)

Cheers!
 
I think you guys are reading too much into this problem. Yes, the board could be arbitrarily large. It could be the size of the solar system and made out of diamond and it would take her trillions of years, but that's not really a safe assumption.

If it takes her 10 minutes to make one cut, it is logical to assume that it would take her 20 minutes to make two cuts. Changing the size of the board, the sharpness of the saw, and the flow rate of time is probably not going to be helpful.

Edit: Spelling. It's Sunday.
 
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MegaVovaN said:
and



Bingo. Cool math problem. Wrong teacher for saying there is only one answer.

We ASSUME that the 3 boards need to be of same dimensions. Like Dr. Pizza says, I could take a square board, cut it in half and then divide half again. That second cut will be shorter in length.

in fact, I can make 3 pieces in 11 minutes.
1. cut square board near the edge so that you have a rod (10 min)
2. cut the rod (<1 min)

Cheers!
Click to expand...

Or you could just look at the picture beside the question...
 
It took Marie 10 minutes for the first cut, so, being smart, she put the handsaw down, grabbed the circular saw, and made the second cut in 30 seconds.

Final time, 10.5 minutes.
 
That picture is a stock picture, because problem says BOARD, whereas in the picture we have a ROD.

If problem read, "Takes 10 min to cut rod in 2 pieces, how long to cut rod in 3 pieces?"

Then answer would be 20 minutes because 1 cut of the rod takes 10 minutes (and 2 cuts are needed to make 3 pieces).

BECAUSE problem says 'board" and does not tell me that the dimensions of the resulting 3 boards must be same, I am free to make assumptions.
 
BoomerD said:
It took Marie 10 minutes for the first cut, so, being smart, she put the handsaw down, grabbed the circular saw, and made the second cut in 30 seconds.

Final time, 10.5 minutes.
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Marie never used power tools in her life, and accidentally cut herself with the power saw. Result = infinite minutes because she never approached saws and boards since then...(never completed 2nd cut)
 
MegaVovaN said:
Marie never used power tools in her life, but realized that the circular saw would stop this inane time watcher from complaining about how long each cut took. She cut the teacher's head off with the Milwaukee circular saw, shoved the board up her ass, and went to home economics class where they discussed the important art of removing blood stains from clothing...
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FTFY
 
The answer is 20. Teacher is stupid, wanna bet this is public school? I had some rather dumbass teachers too and that was over 30 years ago and they have just gotten worse. It was rather bad in math. Many times I had to explain to the damn teacher HOW I got the answer they had marked wrong only to have them finally realize I was the one actually right.
 
MegaVovaN said:
That picture is a stock picture, because problem says BOARD, whereas in the picture we have a ROD.

If problem read, "Takes 10 min to cut rod in 2 pieces, how long to cut rod in 3 pieces?"

Then answer would be 20 minutes because 1 cut of the rod takes 10 minutes (and 2 cuts are needed to make 3 pieces).

BECAUSE problem says 'board" and does not tell me that the dimensions of the resulting 3 boards must be same, I am free to make assumptions.
Click to expand...

That's a stupid assumption that introduces new variables not given in the original problem.

Assume she gets better at it as she goes along. Assume she has a power saw for the second cut. Assume the grain makes it 10x harder to cross-cut and she has a rip saw.

Given the picture and the space provided for an answer, the most reasonable answer is 20 minutes. Anything else, and you're making shit up to add to the original question to justify your answer.
 
With the picture its 20 minutes. Without the picture it could be 15 minutes. On face value the answer is 20 minutes. But with a more detailed question it could easily be 15 minutes.
 
haha. good on the student. also, teacher is wrong

edit: read previous response on square size boards. both could be right. i was thinking of 2x4s and shit. this thread has become interesting
 
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classy said:
With the picture its 20 minutes. Without the picture it could be 15 minutes. On face value the answer is 20 minutes. But with a more detailed question it could easily be 15 minutes.
Click to expand...

It could just as easily be 10.5 minutes. Use your first cut to cut off a very thin strip. Once you start making assumptions you can make the answer be whatever you want. That isn't the point of the question though.
 
classy said:
With the picture its 20 minutes. Without the picture it could be 15 minutes. On face value the answer is 20 minutes. But with a more detailed question it could easily be 15 minutes.
Click to expand...

In this instance, you don't need a "picture" to get to the correct answer. Read the question word for word and understand what being asked to solve it . Do not add or make assumptions what it is.

I can't imagine getting "15 minutes" as the correct answer. :hmm:

I've encountered "wrong answers" from quizzes I've taken during my school days. At least showing the teacher how you got the answer was always encouraged. Not sure how it's done these days.
 
The correct answer is that both Marie and the teacher need to put down the tools and red pens and get the fuck back in the kitchen where they belong.
 
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