document.write( "Question 1116861: The circumference of a font 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. \n" ); document.write( "
Algebra.Com's Answer #731816 by ikleyn(52864)\"\" \"About 
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\n" ); document.write( "The circumference of a \"highlight%28cross%28font%29%29\" front wheel of a tractor Is two feet less than the circumference of a rear wheel.
\n" ); document.write( "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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\n" ); document.write( "\n" ); document.write( "This problem is,  actually,  VERY SIMPLE.   It  can be solved  and  MUST BE SOLVED  much simpler.\r
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document.write( "Let f be the sircumference of the front weel.\r\n" );
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document.write( "Then the circumference of the rear wheel is (f+2) ft, according to the condition.\r\n" );
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document.write( "The number of rotations of the front wheel on the distance of 3500 ft is  \"3500%2Ff\".\r\n" );
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document.write( "The number of rotations of the rear wheel on the distance of 3500 ft is  \"3500%2F%28f%2B2%29\".\r\n" );
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document.write( "What the condition says about their difference, is THIS EQUATION\r\n" );
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document.write( "\"3500%2Ff\" - \"3500%2F%28f%2B2%29\" = 200.\r\n" );
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document.write( "Divide by 100 both sides. You will get \r\n" );
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document.write( "\"35%2Ff\" - \"35%2F%28f%2B2%29\" = 2.\r\n" );
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document.write( "From this point, I see the solution mentally and momentarily:  f = 5.\r\n" );
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document.write( "But you can complete the solution formally in this way: multiply both sides by f*(f+2). You will get\r\n" );
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document.write( "    35*(f+2) - 35f = 2f*(f+2)\r\n" );
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document.write( "    35f + 70 - 35f = 2f^2 + 4f\r\n" );
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document.write( "    2f^2 + 4f - 70 = 0\r\n" );
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document.write( "    f^2 + 2f - 35 = 0\r\n" );
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document.write( "    (f+7)*(f-5) = 0.\r\n" );
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document.write( "The only positive root f = 5 is the solution to the problem.\r\n" );
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\n" ); document.write( "To see many other similar solved problems,  look in the lesson\r
\n" ); document.write( "\n" ); document.write( "    - Challenging word problems solved using quadratic equations \r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this textbook under the topic \"Quadratic equations\". \r
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\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-I
\n" ); document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
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\n" ); document.write( "\n" ); document.write( "When you solve any problem in Math,  getting a correct solution is very important.\r
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\n" ); document.write( "\n" ); document.write( "But presenting your solution in a good style is important,  too.\r
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\n" ); document.write( "\n" ); document.write( "In particular,  I believe,  that any school Math problem might be solved in 10 lines.   //   OK,  let say,  in 20 lines,  with good margin.\r
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\n" ); document.write( "\n" ); document.write( "But  40  and more lines is not a good style for the school Math problems.\r
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