### Math teacher's error

It took Marie 10 minutes to saw a board into 2 pieces. If she works just as fast, how long will it take her to saw another board into 3 pieces?

The teacher marked this answer (20 minutes) wrong, and wrote down 15 minutes as the correct answer. Why is the teacher in error?

The teacher marked this answer (20 minutes) wrong, and wrote down 15 minutes as the correct answer. Why is the teacher in error?

## Comments

Wanna bet the math teacher has never sawn anything?

My kid had similar encounter:

If everybody gets the same answer, it has to be right. Is it ? , with a follow-up in part 2 to find out what the answer will be within a given tolerance.

More deeply, though, it is an example of how non-mathematical knowledge is crucial in word problems. The teacher made the same mistake many students make, she plugged the numbers mentioned in the problem into a convenient formula and called it good.

Teaching calculus to engineering students I was dumbfounded to see how many of them could not set up the equations for simple "tanks and pipes" problems. They simply had no notion of how water flows. It seems so basic I was at a loss for words how to begin to explain it.

There's no substitute for a well-labeled diagram when solving any problem.

If I cut a square board in half vertically, then cut one of the resulting pieces in half horizontally, it _will_ be 15 minutes, because the second cut will take half the time of the first cut.

Granted, the teacher was most likely NOT thinking about that, but it does illustrate problems are often not as clear cut (no pun, honest) as you might first think.

thanks

jah

For example: If the board is perfectly square, and of the same width and thickness as the original board, then two perpendicular cuts would take 15 minutes, as the teacher said. But if the board is of a different length, it could take 11 minutes, 3,000 minutes, 2.7 minutes, or any number of minutes you would care to put down. All answers are correct. :)

If the board is a flat circle, with thickness the same as that of the original board and radius equal to half the width of the original board, then three cuts from equidistant points on the circumference to the center would result in three equal pieces and this would take 15 minutes... but the problem didn't exactly so stipulate, did it? Interesting.

but if we look at it with a proportionally way it will be 15

the time needed will be ( 3 multiplying by 10 divided by 2 )

but i do not accept that way

logic is better even though it is wrong