A carpenter got given some free wooden planks. Some are 12m long and some are 18m long. She wants to cut them up so that she has equal size planks to make using them easier. What size planks should she cut them into to avoid wasting any wood?
12 = 2*6
18 = 3*6
of course she could cut them into 2 or 3 foot lengths, but for min waste use the biggest common factor
I would say 12m because you can't cut a 12m plank into something like a 16 meter plank but you can cut a 18m plank shorter to make it 12m long.
This question makes very little sense to me.
I suppose they are after a length of 6 m, since 12/6 and 18/6 are whole numbers
(but so would length of 3 m)
But the length of a board does not have anything to do with whole numbers,
e.g. a board of length 6.5 m is just as good a board as one of 6 m.
Why not keep the boards as they are and cut them as needed?
Furthermore the question avoids the real situation of loss of wood due to the saw cut.
Lastly, what the heck does "got given" mean ?
so you waste all the six footers?
LOL, carpenters want the max that fits on the truck for min waste on the site.
To determine the size of the planks the carpenter should cut them into, we need to find the greatest common divisor (GCD) or highest common factor (HCF) of 12m and 18m. The GCD will be the length of the planks that will avoid wasting any wood since it will evenly divide both lengths.
To find the GCD, we can use the Euclidean algorithm. Here's how it works:
1. Write down the two lengths: 12m and 18m.
2. Divide the larger length (18m) by the smaller length (12m) to get the quotient and remainder.
- 18m ÷ 12m = 1 remainder 6m
3. Write down the division as an equation: 18m = 12m × 1 + 6m.
4. Now, take the smaller length (12m) and the remainder (6m) and repeat the process.
- 12m ÷ 6m = 2 remainder 0
5. The process stops when the remainder becomes zero. The divisor at this step (6m) is the GCD.
- GCD(12m, 18m) = 6m
Therefore, the carpenter should cut the wooden planks into 6m lengths to avoid wasting any wood.