How many pieces?

Algebra Level 1

It took Marie 10 minutes to cut a board into 2 pieces. If she works just as fast, how long will it take for her to cut another board into 3 pieces? (Assuming you can only cut any piece into half)

Image credit: Flickr Oregon Department of Transportation


The answer is 20.

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25 solutions

Aryan Gaikwad
Feb 14, 2015

Think about it in this way -

------------------------------- 0 cuts/1 piece/0 minutes

---------------|--------------- 1 cut/2 pieces/10 minutes

------|------------|----------- 2 cuts/3 pieces/20 minutes

Aditya Paul
Feb 18, 2015

If all three cuts are lengthwise then only the answer is right. But imagine the board is cut through the middle and again one of these pieces is cut breadth-wise then it comes to 15 minutes. There should be a bit more description regarding how the board is cut.

Isn't it just 10 min per piece halving cut? Thus 20 min either direction?

August Ibekilo - 6 years, 3 months ago

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I believe the thought is here that yes, of a 14 x 6 x 1 is cut long way, slowly and carefully, it says it takes 10 minutes to cut 14ft. Now if you switch the blade to only cut the 6" direction, to make a half, they are saying it wouldn't take 10 minutes as the distance is 1/28th shorter to travel with the saw.

Michael Angel - 4 years, 10 months ago

It would depend on the... ratio of the board's dimensions. If the board was 10x4m and you cut it first into 2pcs of 10x2m each (in 10min, with the speed of 1m per minute), the next cut was 10x2m into 2x 5x2m pcs (2m of cut edge), you will get 12 minutes.

Piotr Skonieczka - 2 years, 5 months ago
Rahul Gampa
Feb 16, 2015

1 cut = 2 pieces, 2 cut = 3 pieces, 1 cut = 10 min, 2 cut = 10 *2 min = 20 min

Sravanth C.
Feb 15, 2015

cool question dude..................................

Lakshya Gupta
Feb 15, 2015

It took her 10 minutes to make one cut (2 pieces). It will take her 20 minutes to make 2 cuts (3 pieces).

Cameron Callaghan
Feb 17, 2015

Pieces-1*10=time

(Pieces-1) × 10 = time

Kaleb De la Garza - 5 years, 7 months ago
Phạm Nhung
Feb 25, 2015

Need 1 cut to have 2 pieces, it takes 10 mins

Need 2 cut to have 3 pieces, it takes 10*2 = 20 mins

Cole Wyeth
Feb 17, 2015

It's the number of cuts times 10... But I have a grievance against this problem: What if the second board is smaller? What if the second board is the same size, but the second cut is shorter because it had a small piece cut off?

Suprem S.Nalkund
Mar 16, 2015

Nice question man

Afzaal Aslam
Feb 24, 2015

The problem is If she works just as fast, that means that if she cuts with the same speed...

v⃗ =△x⃗ △t⃗

If Marie saw a board into 2 pieces in 10 minutes, that means 1 cut in 10 minutes (v⃗ =110 cuts per minute ).

So to perform 2 cuts to obtain 3 pieces, we have:

△t⃗ =△x⃗ v⃗ =2(110)=2×10=20

But think in a table with 30 height per 15 width, if she cuts from bottom up, dividing the table into the middle with two pieces of 30 height per 7,5 width, and then cut again, but this time she cuts from left to right, and then she gets two pieces with 15 height per 7,5 of width, thus she will spend 10 minutes on the first cut, plus 5 in the other, since it's half of the table width. I think that it should have more detailed description.

Rafael Nunes - 6 years, 2 months ago
David Bloom
Feb 23, 2015

(Time for all Cuts) = (# of Cuts) * (Time for One Cut)

Y = X * Y1

Y = (2) * (10)

Y = 20 Minutes.

Or you could just USE YOUR FREAKING BRAIN! Idiots...

Kevin Liu
Oct 27, 2020

Notice that when Marie cuts a board into n n pieces, there are n 1 n - 1 cuts.

Therefore, from the question, 1 1 cut ( 2 2 pieces) takes 10 10 minutes. 2 2 cuts ( 3 3 pieces) must then take 10 × 2 = 20 10 \times 2 = \boxed{20} minutes.

Shay Maayan
Jun 16, 2019

10 minutes = 2 pieces 0 minutes = 1 piece We can see that it takes Marie 10 minutes to add a piece. 10 + 10 = 10 x 2 = 20. It is 10 x 2 Because we want 3 pieces and it takes 10 minutes for a piece to add. You might think it's 30 then, Because 10 + 10 + 10 = 10 x 3 = 30. But it's not, Because we start already with 1 piece and it took no time for the first piece.

Conclusion: Marie can cut a board into 3 pieces in 20 minutes. So it equals 20 .

  • Apply what you know about cutting something into pieces. Here, 2 pieces means 1 cut, so 3 pieces means 2 cut: N parts = N-1 cuts . It took 10 minutes for Marie to cut 1 piece, therefore it'll take 20 minutes to cut 2 times to get 3 pieces.
Sachin Anand
Apr 18, 2015

Cutting the same board along it's cross section has nothing to do with the size of the piece.

Heidi Van De Wege
Mar 22, 2015

Each cut is 10 minutes and makes two board pieces. Making three cuts takes 20 minutes ( 10 minutes for each cut) and makes three board pieces.

Vignesh Rao
Mar 18, 2015

First she can cut the board into pieces then she gets 1 × 2 = 2 1 \times 2=2 pieces which will take 10 10 minutes

Then she can cut one of the two pieces into 2 2 which will take another 10 10 minutes. Totally, time taken= 10 + 10 = 20 10+10=20 minutes

Lutfar Robin
Feb 22, 2015

---/-----/------- 2 cut needs 20 min

Refath Bari
Feb 22, 2015

Think about it this way: If she takes 10 Minutes (she's so SLOW!) to break the board in half(you can't break the board in 1 peice,by the way,because that's how it starts off),then we can make an expression:

10 n : n ,being the number of times she cuts the board If she cuts the board twice,once in half and then cuts the board again: 10(1)+10(1)=10+10=20 Minutes!

Mitch Malakhov
Feb 22, 2015

since you can only cut a board in half regardless of the size of the board it would have to take 20 minutes. cutting one board in half takes 10 minutes. taking a half of the board which you cut and cutting that in half takes another 10 minutes. 10+10=20 :)

Saleh Fs
Feb 19, 2015

As 2 pieces require 10 minutes, then keeping 1 piece, take the other, then cut this, it will also takes 10 minutes, so total time requires 20 minutes.

Doodlebug Spencer
Feb 18, 2015

well it does say that boards can only be cut in half so 1 cut 2 halves = 10 minutes then you cant acutaly create exactly 3 you create 4 but that is your awser

Manish Meena
Feb 18, 2015

It takes 10 minutes to make a single cut for two pieces. And for 3 pieces it would require 2 cuts. So, 1 cut= 10mins Therefore 2 cuts= 20mins

Gagan Raj
Feb 16, 2015

In this problem its not about the number of pieces , its about the number of cuts.

She takes 10 minutes for 1 cut i.e. 2 pieces.

Thus if she works just as fast for cutting 3 pieces then she would take 20 minutes as she has to perform 2 cuts.

For one cut she takes 10 minutes and thus for 2 cuts i.e. 3 pieces she has to take double the time.

Thus she takes up 20 minutes.

Fox To-ong
Feb 16, 2015

her rate is = to 10 min per cut, thus to make 3 pcs. it need 2 cuts so 2x 10 = 20 minutes.

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