Lagunitas Brown Shugga

Lagunitas Brewing Company, Petaluma, California
Brown Shugga
American Strong Ale
9.99% ABV
12 oz bottle (for two)

Question: How can the experience of grading 40 homeworks on proportions and fractions be made better?
Answer: By trying to review four different beers at the same time.

The second in this afternoon’s lineup is a jewel among strong beers. Perrinator declares this to be one of the best beers he has had in a while. It is brewed with cane sugar, but while sweet, it is not at all cloying. More importantly, it is insanely hoppy.

All I can handle of this assertively flavorful beer is half of the bottle, but I’m not saying that’s a bad thing. And due to its alcohol content (which it conceals-and-carries well), a half bottle is all I can drink while still wielding my red pen with some degree of legibility.

Below I’ve rephrased a (well-known?) question on my students’ homework. It’s extra credit, so don’t be dismayed if you can’t get the answer. I will accept solutions in the comments. (Note: due to my beer-themed rephrasing, it sounds like slave labor. I’m not advocating slavery. I can’t emphasize this enough, people. NO SLAVES.)

A farmer puts six hops-harvesters into a hop field and leaves them there until they harvest all the hops. This takes 3 days. She allows the hops to grow back, and then puts three hops-harvesters in the field. This time it takes 7 days for the hops-harvesters to harvest all the hops. But the hops-harvesters all harvested the same amount of hops (as each other and on different days). How is this possible? How long should it take for one hops-harvester to harvest all the hops in the field?

MATH ATTACK!

 

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~ by nininja on January 25, 2011.

22 Responses to “Lagunitas Brown Shugga”

  1. Is it 25 days for one worker? It seems like one of those problems where the remainder carries over and forces you to count another day.
    Now my brain hurts 😦

    • 25 days is the wrong answer. And since you didn’t show your work, I can’t even give you partial credit. ZERO POINTS FOR YOU! Just kidding. It’s not about points.

  2. … uh…. what was the middle part again…?

  3. Is this audible? I think the answer’s in here:

    How many of those thread thingies that carry genes in a linear order does a mule have?
    When did Julius Caesar become Rome’s greatest bridge-maker?
    Hops grow back.

  4. Where can a soul find sweet release? Is endless sleep the next beer?

  5. ok, I’m going to reveal myself as having lost ALL mathematical ability. I’m also pretty stressed out.
    Let H = total amount of hops in the field
    let m = the amount of hops/day harvested by a hops harvester
    The 3 * 6 * m = H (it takes 3 days for 6 machines to harvest the hops)
    and 7 * 3 * m = H (it takes 7 days for 3 machines to harvest the hops)
    but there’s no way to solve this! No wonder I dropped out of grad school! Help!

  6. If hops do not grow:
    Scenario 1
    Six harvesters take three days.
    Each harvester does 1/18 of the hops field each day.
    One harvester would take 18 days.

    If hops do not grow:
    Scenario 2
    Three harvesters take seven days.
    Each harvester does 1/21 of the hops each day.
    One harvester would take 21 days.

    So we know the hops grow.

    1/HOPS = the portion of hops growing back in one day.
    3/HOPS = the portion of hops growing back in three days (Scenario 1)
    7/HOPS = the portion of hops growing back in seven days (Scenario 2).

  7. DG = number of days for one harvester to harvest all the hops if the hops don’t grow.
    In one day, one harvester harvests 1/DG of the hops.
    In one day, six harvesters harvest 6/DG of the hops.
    In one day, three harvesters harvest 3/DG of the hops.

    In three days, all the hops are harvested: 18/DG – 3/HOPS = 1 Complete Harvest
    → 6/DG – 1/HOPS = 1/3 Harvest

    In seven days, all the hops are harvested: 21/DG – 7/HOPS = 1 Complete Harvest.
    → 3/DG – 1/HOPS = 1/7 Harvest

  8. Scenario 1 – Scenario 2:
    3/DG = 4/21 → DG = 63/4, with HOPS = 21
    Assuming uniform rate of growth, yadda yadda, the the number of days for all the hops to grow back is 21.

  9. ƿש = number of days for one harvester to harvest all the hops while the hops grow back.
    ƿשƿשƿשƿשƿשƿשƿשƿשƿשƿשƿשƿשƿשƿשƿשƿשƿשƿשƿשƿשƿשƿשƿשƿשƿשƿשƿשƿשƿשƿשƿשƿש
    ^ does that look vegetable?

  10. Don’t use the Hebrew shin. It makes things flip to right-left.
    ƿ = number of days for one harvester to harvest all the hops while the hops growS back.
    In ƿ days, the harvester harvests ƿ/DG = ƿ/63/4 = 4ƿ/63 of the hops.

    • Everything looks right up to this point! So what is D equal to???? You haven’t used the fact that in D days, D/21 of the field of hops has grown back.

  11. ƿ’s a wynn.
    In ƿ days, all the hops are harvested: 4ƿ/63 – ƿ/21 = 1 → (lcm 63) 4ƿ – 3ƿ = 63
    ƿ = 63

  12. = what I said on January 26, 2011 at 6:22 pm

  13. ^Yes. That song. I couldn’t get audio and didn’t want the answer in the title. My apologies.
    More math + beer!
    Also, what do I win (wynn)?

  14. I’m jelly.
    What do I get if I post a video about spiders?

  15. Extra credit:
    How many harvesters are needed to harvest the field in one day?

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