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Math Help - Word Problem involving conversion

  1. #1
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    Word Problem involving conversion

    Hello

    I was given the following problem and have come up with what i believ to be the correct answer. I would appreciate it if someone could proof read my answer for accuracy.

    1 yard = 0.9144 meters

    1 mile = 1609 meters

    if the area of a piece of land is 3.3 square-miles, then how much is it in square-yards?

    In order to determine the are we must find the length of two sides of the area in question.

    Therefore miles for one side of our area.

    So we can multiply 1.82 miles by 1609 meters to convert statute miles to linear meters

    linear meters

    Now that we have the linear meters for one side of our square area we can Utilizing the formula for area to determine the are in square meters.



    The result is 8575409.4 square meters

    We can now convert square meters to square yards by dividing 8575409.4 square meters by 1.195985 square yards because 1.195985 square yards is equivalent to 1 square meter.



    The final result is 7170164.6 square yards

    So there is 7170164.6 square yards in 3.3 square miles
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  2. #2
    Super Member malaygoel's Avatar
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    Quote Originally Posted by pashah
    Hello

    I was given the following problem and have come up with what i believ to be the correct answer. I would appreciate it if someone could proof read my answer for accuracy.

    1 yard = 0.9144 meters

    1 mile = 1609 meters

    if the area of a piece of land is 3.3 square-miles, then how much is it in square-yards?

    In order to determine the are we must find the length of two sides of the area in question.

    Therefore miles for one side of our area.

    So we can multiply 1.82 miles by 1609 meters to convert statute miles to linear meters

    linear meters

    Now that we have the linear meters for one side of our square area we can Utilizing the formula for area to determine the are in square meters.



    The result is 8575409.4 square meters

    We can now convert square meters to square yards by dividing 8575409.4 square meters by 1.195985 square yards because 1.195985 square yards is equivalent to 1 square meter.



    The final result is 7170164.6 square yards

    So there is 7170164.6 square yards in 3.3 square miles
    You need not necessarily find length and breadth.
    These type of problems you will find frequently in physics and I am giving here a method for it.
    3.3miles^2=3.3 mile*mile
    =3.3yard^2*\frac{miles^2}{yards^2}(since we have to convert into yard squared)
    =3.3yard^2*\frac{miles^2}{meter^2}*\frac{meter^2}{  yard^2}(since we don't any relation betwween yard and mile)
    =3.3yard^2*1609^2*0.9144^2
    =7143292.97yard^2

    Keep Smiling
    Malay
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  3. #3
    MHF Contributor Quick's Avatar
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    Quote Originally Posted by malaygoel
    You need not necessarily find length and breadth.
    These type of problems you will find frequently in physics and I am giving here a method for it.
    3.3miles^2=3.3 mile*mile
    =3.3yard^2*\frac{miles^2}{yards^2}(since we have to convert into yard squared)
    =3.3yard^2*\frac{miles^2}{meter^2}*\frac{meter^2}{  yard^2}(since we don't any relation betwween yard and mile)
    =3.3yard^2*1609^2*0.9144^2
    =7143292.97yard^2

    Keep Smiling
    Malay
    You know, its a good idea to check your equations by turning in measureing units to variables.

    m_i=\text{miles}
    m_e=\text{meters}
    y=\text{yards}

    now let's type in malaygoels equation...

    =3.3y^2*\frac{m_i^2}{m_e^2}*\frac{m_e^2}{y^2}

    multiply: =3.3\frac{m_i^2m_e^2y^2}{m_e^2y^2}

    divide: =3.3\frac{m_i^2\not{m_e^2}\not{y^2}}{\not{m_e^2}<br />
\not<br />
{<br />
y^2}}

    =3.3m_i^2

    tsk, tsk, now I'm wondering how malaygoel got a different answer with that equation...
    Last edited by Quick; July 14th 2006 at 04:18 AM.
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  4. #4
    Super Member malaygoel's Avatar
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    Quote Originally Posted by Quick
    the real equation is...

    =3.3m_i^2

    =3.3m_i^2\times\frac{y^2}{m_i^2} why would I multiply by that fraction you ask? becuase now the miles will cancel out and I'll be left with yards
    Please check the quoted equation

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    Malay
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  5. #5
    MHF Contributor Quick's Avatar
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    Quote Originally Posted by malaygoel
    Please check the quoted equation

    Keep Smiling
    Malay
    That equation is correct and it is different than yours since you put miles^2 per yard^2.

    Unfortunately, the rest of my work (which I edited out) is incorrect. However, so is yours...
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  6. #6
    Eater of Worlds
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    How many square yards are in 3.3 square miles?. Is that the question?.

    There are 640 acres in 1 square mile and 4840 square yards in an acre.

    (640)(3.3)(4840)=10222080 square yds in 3.3 sq. miles.
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  7. #7
    Super Member malaygoel's Avatar
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    Quote Originally Posted by Quick
    That equation is correct and it is different than yours since you put miles^2 per yard^2.

    Unfortunately, the rest of my work (which I edited out) is incorrect. However, so is yours...
    Your equation is wrong
    Verify: 1mile =2 yard(suppose)
    You will find your equation gives wrong answer but mine is correct.
    I arrived at a different answer from pahsah because the original poster has approximated the value of \sqrt{3.3} but I haven't approximated anything.

    Keep Smiling
    Malay
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  8. #8
    MHF Contributor Quick's Avatar
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    Quote Originally Posted by galactus
    How many square yards are in 3.3 square miles?. Is that the question?.

    There are 640 acres in 1 square mile and 4840 square yards in an acre.

    (640)(3.3)(4840)=10222080 square yds in 3.3 sq. miles.
    You know you should really read the question...I'm also surprised at your use of acres (I always forget the measurment for them)

    but no that is not the question in entirety, here Iis the equation...(will someone else take the time to explain it)

    =3.3miles^2\times\left(\frac{1609meters}{1mile}<br />
\right)^2\times\left(\frac{1.093613298yards}{1mete  r}<br />
\right)^2

    Quote Originally Posted by Malay
    Your equation is wrong
    Verify: 1mile =2 yard(suppose)
    You will find your equation gives wrong answer but mine is correct.
    I arrived at a different answer from pahsah because the original poster has approximated the value of \sqrt{3.3} but I haven't approximated anything.

    Keep Smiling
    Malay
    alright lets see...lets try finding yards (m=miles and y=yards)

    malay's equation:
    =1m
    =1y\times\frac{m}{y}
    =1y\times\frac{1}{2}\frac{m}{y}
    =\frac{1}{2}m

    oh look, your equation turned yards into miles quite nicely, except wait! we were trying to turn miles into yards weren't we?

    my equation:
    =1m
    =1m\times\frac{y}{m}
    =1m\times2\frac{y}{m}
    =2y

    tsk tsk, looks like I win
    Last edited by Quick; July 14th 2006 at 05:09 AM.
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  9. #9
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by pashah
    Hello

    I was given the following problem and have come up with what i believ to be the correct answer. I would appreciate it if someone could proof read my answer for accuracy.

    1 yard = 0.9144 meters

    1 mile = 1609 meters

    if the area of a piece of land is 3.3 square-miles, then how much is it in square-yards?

    In order to determine the are we must find the length of two sides of the area in question.

    Therefore miles for one side of our area.

    So we can multiply 1.82 miles by 1609 meters to convert statute miles to linear meters

    linear meters

    Now that we have the linear meters for one side of our square area we can Utilizing the formula for area to determine the are in square meters.



    The result is 8575409.4 square meters

    We can now convert square meters to square yards by dividing 8575409.4 square meters by 1.195985 square yards because 1.195985 square yards is equivalent to 1 square meter.



    The final result is 7170164.6 square yards

    So there is 7170164.6 square yards in 3.3 square miles
    Children! Behave yourselves!

    \frac{3.3 \, mi^2}{1} \times \left ( \frac{1609 \, m}{1 \, mi} \right ) ^2 \times \left ( \frac{1 \, yd}{0.9144 \, m} \right ) ^2

    = \frac{3.3 \cdot 1609^2}{0.9144^2} \, yd^2 \approx 10217710 \, yd^2

    End of story.

    -Dan
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  10. #10
    MHF Contributor Quick's Avatar
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    I would like to point out my equation of =3.3miles^2\times\left(\frac{1609meters}{1mile}<br />
\right)^2 \times\left(\frac{1.093613298yards}{1meter}<br />
\right)^2 is still correct
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  11. #11
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    Hello, pashah!

    1 yard = 0.9144 meters
    1 mile = 1609 meters

    If the area of a piece of land is 3.3 square-miles,
    then how much is it in square-yards?

    I think they threw in the metric conversions to make you work harder.

    If you happen to know miles-to-yards, we can convert directly.


    Since 1\text{ mile} = 1760\text{ yards}, we have: 1\text{ mile}^2 = 1760^2\text{ yd}^2

    Then: . \frac{3.3\text{ mile}^2}{1} \times \frac{1760^2\text{ yd}^2}{1\text{ mile}^2} \;= \;10,222,080\text{ yd}^2

    ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

    Doing it "their" way, the answer is quite inaccurate.

    . . . . 1\text{ mile} = 1609\text{ meters}\quad\Rightarrow\quad 1\text{ mile}^2 = 1609^2\text{ meters}^2

    . . 1\text{ yard} = 0.9144\text{ meters}\quad\Rightarrow\quad 1\text{ yard}^2 = 0.9144^2\text{ meters}^2


    Then we have: . \frac{3.3\text{ miles}^2}{1} \times \frac{1609^2\text{ meters}^2}{1\text{ mile}^2} \times \frac{1\text{ yard}^2}{0.9144^2\text{ meters}^2}

    . . which gives us: . 10,217,710.5\text{ yard}^2


    Their answer is off by nearly the area of a football field.

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  12. #12
    Super Member malaygoel's Avatar
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    Quote Originally Posted by malaygoel
    You need not necessarily find length and breadth.
    These type of problems you will find frequently in physics and I am giving here a method for it.
    3.3miles^2=3.3 mile*mile
    =3.3yard^2*\frac{miles^2}{yards^2}(since we have to convert into yard squared)
    =3.3yard^2*\frac{miles^2}{meter^2}*\frac{meter^2}{  yard^2}(since we don't any relation betwween yard and mile)
    =3.3yard^2*1609^2*0.9144^2
    =7143292.97yard^2

    Keep Smiling
    Malay
    Quick, my method is right. I got the wrong answer because I made the wrong substitution(I used 1 meter= 0.9144 yards)

    Keep Smiling
    Malay
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  13. #13
    MHF Contributor Quick's Avatar
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    Quote Originally Posted by malaygoel
    Quick, my method is right. I got the wrong answer because I made the wrong substitution(I used 1 meter= 0.9144 yards)

    Keep Smiling
    Malay
    YOUR EQUATION IS WRONG!!! tell me something Malay, are there 1609 miles in a meter?

    ~ Q\!u\!i\!c\!k
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  14. #14
    Super Member malaygoel's Avatar
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    Now, I have got it. We are doing the same thing but from different approach.

    We know that 1 foot=12 inch.
    Now we have to convert 3 feet into inches

    Your method:
    3 ft= 3 ft .1 = 3ft. 12in/1ft = 36 in.

    My method:
    3 ft = 3ft.1 = 3ft. in/in = 3in. ft/in = 3in. 12in/in =36in

    Quote Originally Posted by Quick
    YOUR EQUATION IS WRONG!!! tell me something Malay, are there 1609 miles in a meter?

    ~ Q\!u\!i\!c\!k
    I have done mile/meter=1609 because 1 mile = 1609 meter.

    Keep Smiling
    Malay
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  15. #15
    MHF Contributor Quick's Avatar
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    Quote Originally Posted by malaygoel
    Now, I have got it. We are doing the same thing but from different approach.

    We know that 1 foot=12 inch.
    Now we have to convert 3 feet into inches

    Your method:
    3 ft= 3 ft .1 = 3ft. 12in/1ft = 36 in.

    My method:
    3 ft = 3ft.1 = 3ft. in/in = 3in. ft/in = 3in. 12in/in =36in
    Your method is strange but correct.

    I have done mile/meter=1609 because 1 mile = 1609 meter.

    Keep Smiling
    Malay
    umm...why do you keep substituting different measurements into your equation. Why not just do ratios?

    ~ Q\!u\!i\!c\!k
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