Word Problem involving conversion

**pashah** · July 13th 2006, 07:26 PM

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

**malaygoel** · July 13th 2006, 07:49 PM

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

**Quick** · July 14th 2006, 04:06 AM

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: $=3.3\frac{m_i^2\not{m_e^2}\not{y^2}}{\not{m_e^2} \not { y^2}}$

$=3.3m_i^2$

tsk, tsk, now I'm wondering how malaygoel got a different answer with that equation...

**malaygoel** · July 14th 2006, 04:15 AM

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

Keep Smiling
Malay

**Quick** · July 14th 2006, 04:21 AM

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...

**galactus** · July 14th 2006, 04:21 AM

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.

**malaygoel** · July 14th 2006, 04:25 AM

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

**Quick** · July 14th 2006, 04:29 AM

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)

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

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

**topsquark** · July 14th 2006, 04:52 AM

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

**Quick** · July 14th 2006, 05:08 AM

I would like to point out my equation of $=3.3miles^2\times\left(\frac{1609meters}{1mile} \right)^2$ $\times\left(\frac{1.093613298yards}{1meter} \right)^2$ is still correct

**Soroban** · July 14th 2006, 05:13 AM

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.

**malaygoel** · July 14th 2006, 06:50 PM

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

**Quick** · July 14th 2006, 07:59 PM

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?

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

**malaygoel** · July 14th 2006, 08:32 PM

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

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

**Quick** · July 14th 2006, 08:40 PM

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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