# mistressEVIL

repeats again what's already been said

## Practically correct

Bashi_B passed me this math teacher fail picture:

But me and GODJonez came to a conclusion that 15 minutes is practically correct answer:

GODJonez: eh
GODJonez: that's cheating!
mistressEVIL: hmm wait, 15 COULD be correct answer
mistressEVIL: because Marie would already have technique on how to saw really fast developed
GODJonez: bent saw
GODJonez: it saws from two places at the same time but it is a bit harder to use, so it takes a bit longer
GODJonez: or just two saws
mistressEVIL: so PRACTICALLY 15 mins is correct answer.

Theoretically, of course, it is not.

Joonas Lehtolahtigodjonez Wednesday, October 6, 2010 4:20:58 PM

In defense of the teacher let's take a look at the task in a pedantic scientific way.

To be able to answer that question at least, one needs to make a lot of assumptions (some that you do automatically without even thinking about it). First assumption here is that the question is written in (American) English. Of course one could define a language with words written the same way as common English words but with different meanings, changing the task in hand completely. So we'll assume English to understand the question.

The information we know from the text, then, is that it takes 10 minutes to saw a board into 2 pieces. And the question is how long does it take to saw a board into 3 pieces if Marie is working as fast. Now the problem is that the task does not define what the "as fast" is referring to. Naturally it would mean that some sort of speed-like quantity will stay constant. But this speed is not defined and therefore an assumption is needed for what is meant with the speed in this case.

The natural assumption would of course be that the speed is referring to number of cuts in a time unit, so the speed in this case is 1 cut per 10 minutes. With that speed staying constant, then for 3 pieces you need two cuts and hence the time required would be 20 minutes which is what was answered in the paper.

The speed could be defined differently, though, as the teacher has done. The teacher used number of pieces per time unit as the speed, so in this case 2 pieces in 10 minutes = 1 piece in 5 minutes. By keeping this speed constant, it will take 15 minutes for 3 pieces. Of course if you keep this speed constant, the speed for number of cuts per time unit is not constant. And in the first case with answer 20, the number of pieces per time unit is not constant.

So yeah, the question itself is ambiguous and lacking necessary definitions to give simple unambiguous correct answer. Actually, the teacher's assumption of speed quantity is better since for that the starting values are exactly given (2 pieces, 10 minutes). For cuts per time unit one again needs to assume it takes exactly 1 cut to increase number of pieces by 1 and that initially there was already 1 piece (well, that is obvious).

But what about 4 pieces of wood? How long would that take? It would take 20 minutes in both cases, since you can actually 2 separate pieces of wood at the same time provided that the saw is big enough compared to the size of the wood pieces, so first 10 minutes to halve the full board, then another 10 minutes to split both of those at the same time. That means that by keeping the number of cuts constant, it is actually possible to make both 3 and 4 pieces of wood in the exact same time

ernesteban Monday, January 24, 2011 4:00:18 PM

Yeah, not really. With a given speed to saw, you can only saw that much in a given time. If "that much" doubles, be it vertically or horizontally, the time to saw the double amount of the first given quantity of wood is also doubled. So it doesn't matter if you put the two pieces of wood next to each other or underneath each other, it would take twice the time compared to what it would take to saw only one piece.

The mistake you make is that the speed to saw something is only expressed in the depth it can saw. That's not really correct, since the displaced volume of shredded wood is what's defining the speed, and that doubles no matter how to place the two pieces of wood together.

A simple visualisation of this fact: if you would saw a very thin piece of wood while you hold it upright, the saw would go down very fast, because the total volume displaced isn't very much for every centimeter your cut get's deeper. On the other extreme, a very thick piece of wood would require a lot more time to get sawed in two, because the volume is quite large for every centimeter the cut gets deeper.

Unregistered user Monday, January 24, 2011 11:52:38 PM

Anonymous writes: Yes but the speed *always* constant. She works just as fast, although she may be doing significantly more work.

ernesteban Sunday, February 6, 2011 5:35:48 PM

A speed is the word for achieving, attaining or reaching something in a given period of time.

I just explained that "the speed of sawing anything" shouldn't be expressed in meters per second (the depth of the cut), but in meters³ per second (the displaced volume of the wood that was where the cut now is).

When using my more realistic definition of speed to saw something, it is clear that the teacher's and Joonas Lehtolahti's answer is wrong and the student's answer is correct.

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