Question 1116861
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The circumference of a {{{highlight(cross(font))}}} <U>front</U> wheel of a tractor Is two feet less than the circumference of a rear wheel. 
In traveling 3500 feet, a front wheel makes 200 more revolutions than a rear wheel. Find the circumference of each wheel.
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This problem is, &nbsp;actually, &nbsp;VERY SIMPLE.  &nbsp;&nbsp;It &nbsp;<U>can be solved</U>&nbsp; and &nbsp;<U>MUST BE SOLVED</U>&nbsp; much simpler.


<pre>
Let f be the sircumference of the front weel.

Then the circumference of the rear wheel is (f+2) ft, according to the condition.


The number of rotations of the front wheel on the distance of 3500 ft is  {{{3500/f}}}.


The number of rotations of the rear wheel on the distance of 3500 ft is  {{{3500/(f+2)}}}.


What the condition says about their difference, is THIS EQUATION

{{{3500/f}}} - {{{3500/(f+2)}}} = 200.


Divide by 100 both sides. You will get 

{{{35/f}}} - {{{35/(f+2)}}} = 2.


From this point, I see the solution mentally and momentarily:  f = 5.


But you can complete the solution formally in this way: multiply both sides by f*(f+2). You will get


    35*(f+2) - 35f = 2f*(f+2)

    35f + 70 - 35f = 2f^2 + 4f

    2f^2 + 4f - 70 = 0

    f^2 + 2f - 35 = 0

    (f+7)*(f-5) = 0.


The only positive root f = 5 is the solution to the problem.
</pre>

Solved.


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To see many other similar solved problems, &nbsp;look in the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/Challenging-word-problems-solved-using-quadratic-equations.lesson>Challenging word problems solved using quadratic equations</A> 

in this site.


Also, you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this textbook under the topic "<U>Quadratic equations</U>". 



Save the link to this online textbook together with its description


Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson


to your archive and use it when it is needed.


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When you solve any problem in Math, &nbsp;getting a correct solution is very important.


But presenting your solution in a good style is important, &nbsp;too.


In particular, &nbsp;I believe, &nbsp;that any school Math problem might be solved in 10 lines.  &nbsp;&nbsp;//  &nbsp;&nbsp;OK, &nbsp;let say, &nbsp;in 20 lines, &nbsp;with good margin.


But &nbsp;40&nbsp; and more lines is not a good style for the school Math problems.