Wednesday, May 2, 2012

Help, Please

Help, please.  Someone who is good at math and figuring out these things, please help.  Because if I think about this any longer, I might hurt myself from banging my head on the wall.

See, I'm trying to figure out how many pieces of picture rail to buy.  I am told that picture rail comes in lengths of 16 feet and 7 feet.  (That 7' length seems odd to me...why not 8 ft??)  At first, I had a what-the-hell attitude towards it:  the room's about 15 by 15, that's 60 feet of picture rail, done.  Then it occurred to me that subtracting the width of the doors and the window might save me some cash.  Um, yeah, because without those I figure I need about 45 feet of rail.  I think.  Or I could be wrong.

Then I got to thinking about how many cuts I would have to make and how many pieces I could get out of each length of rail.  (And by "I", of course I really mean Charlie.)  That's when my head started to hurt.

Hey, let's put it in the form of a word problem.  Some people--not me--are good at those.  That'll make it easier to understand. 

If Jayne is buying picture rail for her front parlor, and the dimensions of the room are as shown in the photo, and picture rail comes in lengths of 7' and 16', how many pieces of picture rail of each length will Jayne need to buy in order to have the least amount of wasted lumber?

Sharpen those pencils.  Click on the photo to bigify it if you need to.  Hum the theme from Jeopardy.  And help me out, please. 


  1. Assuming I read your diagram properly you have two options - buy 3 - 16' sections:
    1 = 115 + 71 = 6" waste
    2 = 94 + 73 = 25" waste
    3 = 49 + 49 + 47 + 23 + 4 + 4 = 16" waste

    or buy 2 - 16' + 2 - 7' sections:
    1 = 115 + 49 + 23 = 5" waste
    2 = 94 + 49 + 47 = 2" waste
    3 = 73 + 4 = 7" waste
    4 = 71 + 4 = 9" waste

    Depends on how accurate your measuring & cutting are. If the price is $0.45 per foot then you are only dealing with $20.70 for 2 of each size or $21.60 for 3 long ones - $.90 difference!

  2. I came up with same math as Cheryl.. You would have enough that you can miter the the corners... Will the small pieces left give you enough to do the corners of the window seat that juts out? If you want it them done too, I would go with the 3x16 foot sections.

  3. Personally I'd get 3 - 16' sections and have a bit of wiggle room.

    You may need a bit extra on the 49" and 4" pieces for mitering those outside corners near the bay window.

    I didn't think of that when I originally figured the amounts - I'm in accounting not carpentry!

  4. Are the 16 foot pieces finger joined? Stay away from that stuff.

    Make sure you really check any 16 footers that you buy. Long pieces can be warped. I've seen some that could go around a corner because they were so warped.

    I'd go with the long pieces.

  5. Just a note, this is one of the types of problem that computers have a really hard time solving. Not that you can't ever be sure you got enough wood, but there's no math method to check and be sure that you're buying the absolute cheapest combination of lengths. You just have to guess and pick one that feels 'good enough'. (Cheryl's look good to me)

    Don't know if that makes you feel any better about having trouble with the numbers.

  6. REMEMBER, measure twice and cut once!!

  7. If you're me, you figure you're going to cut at least ONE of the boards wrong, so you make sure you have at least enough board to correct a mistake. ;-)

    Loved your word problem!