Room is 4.2 m long and the flooring boards run lengthways. The flooring joists (supports) are set out at 400mm centres. All flooring boards must join on a joist. The timber merchant supplies flooring boards in the following lengths:-
2.7 m
3.0 m
3.6 m
3.9 m
In what length(s) should the flooring boards be ordered so that there will be no waste?
Pls explain working out.
400mm = 0.4m
so which length is a multiple of 0.4 ?
To determine the lengths of flooring boards to order without any waste, we need to calculate how many boards of each length are required to cover the room length of 4.2 meters.
Given that the joists are spaced 400mm (0.4m) apart, we can calculate the number of joists required by dividing the room length by 0.4m:
Number of Joists = Room Length / Spacing Between Joists
Number of Joists = 4.2m / 0.4m
Number of Joists = 10.5
Since the number of joists needs to be a whole number, we need to round up to the nearest whole number. Therefore, we will need 11 joists for this room.
Now, let's determine the combination of flooring board lengths that will cover the room without any waste. We can try different combinations of lengths until we find the best fit.
Start with the longest available board length, 3.9m, and determine the number of boards required to cover the room:
Number of 3.9m Boards = Room Length / Length of Board
Number of 3.9m Boards = 4.2m / 3.9m
Number of 3.9m Boards = 1.08
Again, round up to the nearest whole number, so we need at least 2 boards of length 3.9m.
Now subtract the length covered by these boards from the room length:
Remaining Length = Room Length - (Number of 3.9m Boards * Length of Board)
Remaining Length = 4.2m - (2 * 3.9m)
Remaining Length = 4.2m - 7.8m
Remaining Length = -3.6m
Since the remaining length is negative, we cannot use the 3.9m boards alone to cover the room.
Next, try the next longest available board length, 3.6m:
Number of 3.6m Boards = Remaining Length / Length of Board
Number of 3.6m Boards = -3.6m / 3.6m
Number of 3.6m Boards = -1
Again, since the number of boards cannot be negative, we cannot use the 3.6m boards alone to cover the room.
Repeat this process for the shorter board lengths until we find a combination that covers the room without waste.
Now, try the 3.0m boards:
Number of 3.0m Boards = Remaining Length / Length of Board
Number of 3.0m Boards = -3.6m / 3.0m
Number of 3.0m Boards = -1.2
Since we can't have a fraction of a board, we cannot use the 3.0m boards alone.
Finally, try the 2.7m boards:
Number of 2.7m Boards = Remaining Length / Length of Board
Number of 2.7m Boards = -3.6m / 2.7m
Number of 2.7m Boards = -1.33
Again, we cannot have a fraction of a board, so the 2.7m boards alone won't work either.
Based on these calculations, we cannot find a combination of the given board lengths that will cover the room without any waste. You may need to consider different board lengths or consult with the timber merchant for other options.