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Joined: Oct 2011
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Kevin is using wooden rods to make picture frames. The length and width of one picture frame and the length of one wooden rod are shown below:
(diagram of a rectangle with dimensions of 10 inches and 8 inches marked, and a single wooden rod marked with a length of 48 inches)
1) What is the perimeter, inches, of the picture frame? (straight forward -- no complaints there)
2) How many wooden rods does Kevin need if he makes 4 picture frames like the one above?
Well, the only answer they gave credit for was 3 -- perimeter x 4 divided by 48. I wonder how many kids did the calculation you explained to arrive at 3, and how many checked to see whether or not you could actually cut 8 10" pieces and 8 8" pieces from 3 48" rods. It turns out you can (if you ignore losses due to the width of your saw blade and sanding... which would require you to use 4 rods in the real world). At least the question authors got that much right. I didn't worry about sanding or cut width, because in the real world, you wouldn't. This is a picture frame, not a sensitive scientific instrument. And if we assume that this is being done by a skilled worker with high-quality tools, the losses should be near enough to constant so that we still end up with a rectangle. It's that waste at the end that I see as a problem in the real world. If you cut out the lengths you need, you'll have enough wood, but one side of one frame will consist of three waste pieces glued together. It's hideous and unprofessional.
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Joined: Jun 2010
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It's that waste at the end that I see as a problem in the real world. If you cut out the lengths you need, you'll have enough wood, but one side of one frame will consist of three waste pieces glued together. It's hideous and unprofessional. It would be hideous. I think that's why DAD22 checked to make sure it could be done without joining scraps, which it can-- you just can't cut all the rods the same way.
Striving to increase my rate of flow, and fight forum gloopiness.
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It's that waste at the end that I see as a problem in the real world. If you cut out the lengths you need, you'll have enough wood, but one side of one frame will consist of three waste pieces glued together. It's hideous and unprofessional. It would be hideous. I think that's why DAD22 checked to make sure it could be done without joining scraps, which it can-- you just can't cut all the rods the same way. Duh. 6 x 8 = 48. That's me told.
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Joined: Jul 2011
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I didn't worry about sanding or cut width, because in the real world, you wouldn't. This is a picture frame, not a sensitive scientific instrument. And if we assume that this is being done by a skilled worker with high-quality tools, the losses should be near enough to constant so that we still end up with a rectangle. Ending up with a rectangle, and ending up with an 8" x 10" rectangle are not the same thing. My circular saw blade has about 1/8" kerf width. That's rather significant in my book. It's that waste at the end that I see as a problem in the real world. If you cut out the lengths you need, you'll have enough wood, but one side of one frame will consist of three waste pieces glued together. It's hideous and unprofessional. I agree with you that this is the bigger concern. The main point of my post was that you actually CAN cut the rods into 8 8" pieces and 8 10" pieces, and you wont have to join leftover pieces together if you plan ahead. Iucounu already explicitly stated how to do this.
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Don't sweat the kerf as long as it is less than the width of the rods. Presuming you are trying to use the minimum number of cuts and that the corners are 45 degree joins, you'll recover (n-1)*(width of rod)-kerf per rod (where n is number of sections being cut) by alternating cuts.
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Nice catch, Zen Scanner.
Striving to increase my rate of flow, and fight forum gloopiness.
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My DH would want me to emphasize the point that DAD22 has made here-- there is a HUGE difference between framing carpentry (where presumably the kerf would be no big deal) and fine woodworking (cabinetmaking, etc). Generally frame making would fall into the latter category. We really need to know whether or not these frames are going to be filled and painted. What kind of wood is this, hmmm? That might provide us with a clue. Pine or aspen is likely to just be painted, and there we might not care... walnut or some exotic hardwood might be more likely to be used with a translucent finish. The joinery would need to be far more exacting in the latter case. What sort of saw is being used, anyway? Some Japanese saws produce a very tiny kerf, and are ideal for this sort of work. Inquiring minds want to know. PS-- was there any mention of swearing in the original problem? That's generally my clue that my spouse is working to more exacting standards. LOL.
Schrödinger's cat walks into a bar. And doesn't.
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Don't sweat the kerf as long as it is less than the width of the rods. Presuming you are trying to use the minimum number of cuts and that the corners are 45 degree joins, you'll recover (n-1)*(width of rod)-kerf per rod (where n is number of sections being cut) by alternating cuts. Most picture frames are created from wood that is decorative, and asymmetric down the center line, though.
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Joined: Feb 2011
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Right. We really need a visual of the materials, I think. Until then, I'm going with "Not enough information."
Schrödinger's cat walks into a bar. And doesn't.
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We really need to know whether or not these frames are going to be filled and painted. What kind of wood is this, hmmm? That might provide us with a clue. Pine or aspen is likely to just be painted, and there we might not care... walnut or some exotic hardwood might be more likely to be used with a translucent finish. The joinery would need to be far more exacting in the latter case. What sort of saw is being used, anyway? Some Japanese saws produce a very tiny kerf, and are ideal for this sort of work. Inquiring minds want to know. This is why I assumed a high-quality worker and tools for the problem. A saw with a 1/8" kerf for frame making? LOL. Even with the best saws, the kerf will be a non-zero number, as will any losses due to sanding, but they will be miniscule. Also miniscule will be offsetting gains from paint/lacquer, and space for the joint itself, because I'm assuming we're not using some form of molecular bonding.
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