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Homework Help: Confusing Old time Measurements =(

  1. Jan 21, 2010 #1
    1. The problem statement, all variables and given/known data
    A furlong is and old British unit of length equal to 0.125 mi, derived from the length of a furrow in an acre of plowed land. A fortnight is a unit of time corresponding to two weeks, or 14 days and nights. Find the speed of light in megafurlongs per fortnight. (one megafurlong equals a million furlongs).

    2. Relevant equations

    speed= distance/time
    fur=0,125 mi
    for=2 weeks
    mg= 1,000,000 fur

    3. The attempt at a solution

    1 mf/ 1,000,000 fur x 1 fur/0.125 mi x 0.125 mi/ 1fur x 2w/1 for = ... i'm stumped here. i cant understand which way to set it up so that i am only left with mf/for
  2. jcsd
  3. Jan 21, 2010 #2


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    If you are inexperienced with this, I suggest that you do it in steps instead of trying all at once. I will get you started, but you will have to finish.

    You start with what you know. The speed of light is c = 186,000 mile/hr. So you write


    Now you are given that

    [tex]1 mile=\frac{1}{0.125}fu[/tex]

    Put that in the previous expression to get



    [tex]1fu=10^{-6} Mfu[/tex]

    Put that in the expression to get


    Finish the question by proceeding along these lines to get the fortnight in the denominator. Incidentally, you don't really need the 186,000 there. You could as well start with 1 mile/hr to get the conversion factor then multiply the result by 186,000.

    *** Correction ***

    As pointed out by mgb_phys, the speed of light is 186,000 miles/sec. So the conversion is from "sec" to "fortnight". My apologies for the confusion.
    Last edited: Jan 21, 2010
  4. Jan 21, 2010 #3


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    The speed of light in SI units is defined as (approximately) [itex]3 \times 10^8[/itex] m/s.
    How many miles per second is this?
    So how many furlongs per second?
  5. Jan 21, 2010 #4


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    First you need to estimate the answer so you know if you got it right.
    A furlong is less than a mile so a speed in furlongs/hour would be a larger number than mi/hour (ie at the same speed you do more furlongs than you do miles) - just like a speed in km/h is a bigger number than in mph.
    But a fortnigth is much bigger than an hour so at the same speed you would cover a much bigger distance. So the same speed would be a much bigger number in f/f

    Converting is just a matter of fractions.

    Assuming you start in miles/sec (c = 186,000 mi/s)
    furlongs / fortnight = miles/second * ( fortnight/second) / ( furlongs / mile )

    furlongs/mile = 0.125, fortnight/second = 14*24*3600
    So 186,000 * (14*24*3600/0.125) =
  6. Jan 21, 2010 #5


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    kuruman - slight typo, it's 186,000 mi/SECOND

    Teenytiny1991 - using Furlong/Fortnight/Firkin is to teach how to do these sort of conversion. It's just a bit more fun than doing mi/s to m/s or J to eV.
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